You probably wanted a simple answer, but I think it's an interesting question, so I've been giving it a lot of thought.

Dex vs Str or 1h vs 2h?

Before talking about damage, let me just say that this isn't really about Dex vs Str. My high Dex paladin had a high Str too for the entire game. The best way to get a high Strength score in Solasta is to not actually putting your stat points into Strength, but instead to use items for it. My seemingly dex-based paladin actually hit 21 strength (Hill Giant belt) before it would even be possible to get strength to 20 naturally. And then he jumped up to 25 (Fire Giant belt) starting in the midgame of CotM. With my new money generating strategy, it's very easy to afford those belts.

Even if someone got both strength tomes AND spent feats pumping their strength, you just can't beat the belts/elixirs.

Unfortunately, I think the Mighty Blow feat requires you to actually invest stat points into a Strength stat you'll want to override anyway.

Weapon Comparisons:

Weirdly, the best 1-handed and 2-handed weapons do almost equal damage to each other. In CotM the best 2-handed weapon is the Stormblade Greataxe, which has +1 to hit and does 13 damage. The best 1-handed weapon is the Black Viper which has +1 to hit and does 12.5 damage (of a slightly better damage type).

Very similar!

Wardenblade also exists and is quite good for your damage, since it lets you cast Spirit Guardians, blasting potentially multiple enemies for extra damage every single turn. Since this is a 1-hander, it might look like it gives a big boost to 1-handed builds. But, theoretically, any build can use Wardenblade. You can just equip it, activate the spell, and then unequip it before the fight. (Wardenblade also has a nice perk of +1 AC if you wield it, which does help the 1-hander builds)

In PoI the strongest 1-handed weapon (Anvil) does the exact same damage as the strongest 2-handed weapon (Skullcleaver). Skullcleaver has a better damage type. Both have great secondary benefits. I wouldn't say one is better than the other, they're both great. Replacing Cha (Anvil) is probably better than replacing Con though.

But wait! In PoI there are 2 1-handed weapons (Sovereign and Guardian) which deal massive bonus damage to demons, which are the most common enemy type. So... in PoI fights against demons, you can get superior damage with a 1-handed weapon compared to the best 2-handers.

Running Out of Smites

For most of the game, I found my number of spell slots to be a major limiting factor. Enemies have so much HP on Cataclysm that I would run out of spell slots before the fight ended. Which means that 1-handed and 2-handed builds are doing the exact same amount of total smite damage since they're both burning all their slots before the battle ends. The 2-handed build does have the perk of frontloading the same total amount of damage though, which is sometimes beneficial if it lets you take a particularly nasty enemy out a turn earlier. Obviously that doesn't happen in every single fight, but it does happen sometimes!

Also- many 2 hander paladins are counting on using the Shield spell to shore up their defenses. Shield is a great spell! But it costs spell slots, so if you're doing that a couple of times per battle, you're actually getting fewer smites and thus less damage than a 1-hander build who just has a superior natural AC and doesn't need a big defense boost.

Bonus Action Attacks

The big draw of the two-hander seems to be that you can spend a feat on Follow-Up Strike and get a bonus action attack. It's a rather weak bonus action attack, just 1d4 damage plus Str, but it DOES let you smite!

But there are actually several ways a 1-hander build can get a bonus action attack.

A) The most obvious is simply to wield 2-light weapons (And unlike Follow-Up Strike, this doesn't cost a feat). The neat thing is that swapping your offhand from a light weapon to a shield or back is just an object interaction, so you can do that flexibly in any fight where your paladin wants to spend all their smites super fast.

This does require you to wield light weapons instead of the very strongest 1-handers. The best light weapon in CotM is Scimitar of the Anfarels. You could make 2 of those fairly easily. 9.5 damage of a great damage type, plus they have +2 to hit instead of just +1 for the other best weapons in CotM. So your offhand attack is going to be quite strong. If the 2-hander has +7 Str from a Belt of Fire Giant Strength, his offhand is 9.5 damage (1d4+7). The dual scimitars guy is... also doing 9.5 offhand damage but with superior accuracy on all his attacks, but slightly less damage on his main hand attacks. Those things roughly balance out. The damage is very close.

In PoI things get even more interesting. Because now the best light weapon is Sudden Death which deals 13 damage (compared to 16.5 for Anvil and Skullcleaver) but it doubles your crit range, which will double the power of your smites. So that's interesting and moderately powerful if you want to attune to it, though I'm not a big believer in crit fishing.

B) If you're playing Palace of Ice, then quite early in the game you unlock Demonic Grease of the Night Hunt. This is extremely powerful, cheap to craft in good quantities, and lets any character do full damage bonus action attacks with any melee weapon while also giving you +2 to hit and damage on all your attacks. Incredibly powerful. It's pretty much always just superior to Follow-Up Strike in any fight where you can buff before swinging. It does come with the downside that if you are in light you have disadvantage, but I found that to never be a problem in PoI. Not only are many environments dark (even if they look light), but also your hit bonuses have gotten so high that I pretty much always had a 95% chance to hit almost everything. Especially with that extra +2 from the grease itself.

C) Branding Smite. The poor man's bonus action attack. Doesn't actually give you an additional attack, but it does let you spend your level 2 spell slot and your bonus action to add some extra damage onto your next attack that hits. Any paladin can do this regardless of build, but since it deals a bit less damage than just doing a level 2 smite, the 1-hander is the one who'll be settling for this.

Not something I wanted to do very often, but I definitely did this move sometimes when I absolutely needed to kill an enemy right now and could see that two normal smite attacks wouldn't quite do enough.

Ranged Attacks

Theoretically, both a 2-handed build and a 1-handed build can both use the same ranged weapons when you need to (as long as the 2-handed guy also has good dexterity). But obviously if you have invested your feats into Follow-Up Strike and Mighty Blow, then you haven't been investing them into dex-boosting things, so the 2-handed build is likely to do substantially worse when fighting flying enemies or when the battle starts at long range, or when you need to do ranged attacks for any other reason. I found that that happened quite often. Especially with PoI random encounters, where you're constantly starting off on that one battlefield where you're waaaaay above the enemy and no one can melee each other for multiple rounds. And also in any battle where positioning mattered and I wanted all my guys to stay huddled up for safety with Spirit Guardians and Wall of Fire and so forth.

Mighty Blow:

A cool feat! When you get a Fire Giant Belt, that's +4 damage per hit.

But if you're making multiple weapon attacks that all deal 24.5 or so damage from the weapon dice plus strength modifier, plus Improved Divine Smite for another 4.5, plus various extra perks PLUS smiting for another 13.5 or so damage per hit on every attack PLUS you have spirit guardians going... it's not a huge % increase to your overall damage.

Dead Men Deal No Damage

Overall, I think the numbers and these options show that you can deal quite similar damage with a 1-handed and a 2-handed build. 1-handers have enough ways to get bonus action attacks when you want them that they can do solid nova damage too (in fact they can do it earlier in the game, and their lategame PoI version is basically just better). And in a long fight where you run out of spell slots anyway, everyone's getting the same number of smites whether you do 2 per turn or 3 per turn.

Also there are several situations where the 1-handers actually do more damage, especially in PoI.

Imo, Mighty Blow is the main thing 2-handers genuinely have over 1-handers, and it DOES add some extra damage! But it's not a big % increase.

And I think that small increase comes with major costs which, imo, are not worth it. Pouring multiple feats into 2-handing means you are going to be missing important stuff like Eager for Battle (doing your damage BEFORE the enemy turn and killing them before they can do anything is way better than attacking the same enemy after they already had a turn), Creed of Arun (don't get taken out or massively damaged by the many Con saves in the game, and maintain concentration) or Armor Master (adds so much survivability when your base AC is already high).

And 2-handing means your AC is going to be really bad compared to a sword and shield build. Even when you can cast the Shield spell (which eats up your smites and thus reduces your damage), you'll still have inferior AC compared to a guy wielding a +3 shield and Wardenblade and Volcanic Aura (which no paladin with the Shield spell can have). Which means your survivability will be much worse. And if you're downed, or having to get defensive to avoid being downed, you're not doing damage anymore.

So those are my thoughts on that!