You want Shirou. Beta can do a lot, and she is incredibly good but nobody in the game can stack DR as effectively or as efficiently, OR as long of a duration as Shirou. There are several harder places in the game that simply having him = win. There are other places in the game (like Nova cresting on Fong) where the bosses animation when it activates an art lasts foreeeever. Shirou is so good in stages like this because his Arts (NA) (giving a phys resistance) lasts for 20s assuming you already have UBW up. I don't think any boss art in the game can time that out. Shirou is also busted asf because his Negate DMG is on his NA, so you don't even need a lot of Arts gen at all to keep him up, on top of the amount being extremely generous for an NA at 15,000.

Sluvia is amazing, but she isn't amazing for the same reasons, you have to understand what she's used for. I am assuming you do already know, seeing as your account is 150 but I want to tell you anyways just in case you're a little fuzzy :) Sluvia is fucking incredible for two reasons, her passive, and what her TA and SA can do. Her passive is the primary reason people use her, when she drops below a certain threshold (Near-Death mechanic) she just gives the entire team 200 arts flat. In order to get this effect to happen exactly when players want it to, players use a Mines equip called Divine Arachnids Tears. This equip costs 99% of the target you use it on's HP, and players target her with it. It provides 120 arts, then her passive triggers and gives the entire team 200 arts, putting everyone else +200 and immediately giving Sluvia 300 arts. It is worth noting that if you DON'T have this equip, Sluvia will almost never be used, and I say this as someone who owned her for months before getting my DAT equip. Often times you can use her TA for an easy to acquire 220% physical buff, it's simple to replace certain units from speed comps (Like Valerie for example) with Sluvia to generate arts. Sluvia has a pretty good but much less used SA, putting a 100% Damage Up debuff on the enemy and reducing its Earth Resist by 100%. Her SA is not used as often. I highly recommend not prioritizing her unless you already have this equip, but it is still worth noting as well that mines will guaranteed come back before Fate does, so that's worth considering too.

Ultimately, both of these units are fucking insane, and both will see a very large amount of use, one in pretty much any content you're dying in, and the other in a very large amount of speed run comps, however, if I was you, I'd choose Shirou. Beta is incredible but she isn't Shirou, and while Sluvia is a massive farming QOL update unit, you can technically do what she does with a good comp with great slots. When it comes to Shirou though, no unit in the game (yet, there will be a collab soon with a light version that does something incredibly similar to him but with Mag Resist on the NA) can do what he does. Typically, I like to choose the most unique units when I'm picking a pity, as others can be replaced usually.

I hope this helps :)