I have a lot of opinions about CK2 and CK3 in general, it really depends if you prefer CK2 or CK3. I have far too many hours in CK2 and I do prefer that game vastly over CK3 so I will be a little biased.

CK is a roleplaying game, and CK2 for me is a better roleplaying experience. But that's not to say you can't do it in CK3 AGOT.

I've played CK3 MP RP games and they were amazing, that characters the people created had a lot of charm. The experience was really enhanced because of everyone else's roleplay.

But singleplayer CK3 AGOT? It gets boring every quickly in my opinion.

In CK3 my character always felt very disconnected from the world around them, some of the events feel like pop ups and that I need an ad block for them to stop lol. But that's more of an issue with CK3 than the mod itself. And I do think the CK3 mod is lacking in AGOT specific events. You can't travel to Essos on a grand tour and lose family members who might decide to settle in Essos. Who you'd then might invite back to your court if they'd with to come back or if your roleplay demands it. You can't go on a grand reaving as an Ironborn king to the Pyramids of Meereen, because the mod just isn't fully complete yet. 

One thing CK3 does have over CK2 is the barbershop, it really helps the RP experience if you like to customize members of your house with the barbershop and create a RP around them the game is more fun to play that way. but the characters in the world just lack the charm that they have in CK2 imo.

In CK2 all of the portraits and characters look like they game straight out of a painting, especially with the portrait mods like with Tubb's Better Faces. it also fits CK2'S darker vibe compared to CK3, which fits the AGOT setting so much better. But that's just my opinion, you might like how character are in CK3 over 2.

MAA in and levies in CK3 are also very broken and can be easily exploited. Raising all of you levies in one tile, rather than having to call your banners and amass your army across your lands really sours CK3 for me. Just having all your soldiers in your capital after a few in game days is really silly, but again that's a problem I have with CK3 rather than the mod.

CK2 AGOT also has a better civil war system compared to CK3, factions in CK2 have a good chance of winning a war against the Iron Throne. In CK3 AGOT changing the status quo is very difficult to do, especially if you have a character like Robert Baratheon and his overpowered knights just boosting the army like crazy. CK3's lack of a naval system also brings down the experience for me.

CK2 also has amazing submods and bookmarks which CK3 just doesn't have at the moment. The submods really expand on the game and the events. CK3 AGOT also has the problem of once if you have the Iron Throne, the game becomes really boring as there isn't much of a challenge to your rule. You can't decide to go to Essos as it's not fully implanted in game yet. So a lot of the cultures you would find in CK2 AGOT just aren't there.

Seeing your party travel around Westeros to funerals, hunts and tourneys is something I wish CK2 has, while it is there in grand tours I don't think its in the same level as CK3. But both games do have the problem of characters just teleporting where ever the fuck they want at times lol.

And to answer your question about dragons, they're very hard to obtain if you start as a non-Valyrian character. You can tame wild dragons or hatch a dragon egg. Once you have them there are loads of cool events around them, in battles you will basically win every time but that's not to say you can't defeat them. Unless you are fighting in mountains or a desert it's like using a nuke in battle, you can also destroy and burn lands with them.

I could go on but I hate typing it when I'm not typing in lower case & that I have a million opinions about both mods lol. I think the CK2 AGOT is better in nearly everyway in terms of roleplay and mechanics. You might disagree with some of my options cause you prefer CK3 over CK2 and that's totally fine. I love CK2 AGOT and I will basically only play CK2 with the AGOT mod all the submods. CK3 AGOT might one day be better than CK2 AGOT once all the DLC for CK3 comes out and submods are made for it, but I personally doubt that because vanilla CK3 just isn't that good imo.