To give a properly holistic answer to this question, I think DS2 is the better game because it still tries to use encounter design, enemy placement, and environmental hazards, to provide challenge, rather than giving every second enemy unpredictable 7 hit combos and calling it a day. I'm not going to defend some of its shoddy content, but it's the last Souls game with serious dungeon crawler roots, whereas the games after Bloodborne are all just edgy combat simulators, Elden Ring included.
I disagree with this in parts. I agree that DS2 still tries and gives some very good dungeon crawling sense (which I think was severely lost in DS3), but I think Elden Ring found this again. Even if Catacombs, Caves and Mines are small, they still give some tension, but if we speak about the game in general, it's like huge dungeon crawler, one which you can approach in every way you like, and one which the Legacy Dungeons give an extremely satisfying crawling experience.
Let me give you an example of what I mean by this. You complain about bosses in DS2 having limited movesets. Well, one of the hardest bosses in Demon's Souls, the Maneaters, also have like 4 different moves, of which maybe 2 are actually dangerous. So, how are they difficult with such a limited moveset? There's two of them, they can fly, and the fight takes place on a narrow bridge, where you have to constantly be careful of rolling off the ledge or getting knocked off. The way this constrains your mobility and positioning is what makes the fight hard.
I agree completely about Maneaters being an excellent fight using a limited moveset. Then again, this doesn't help DS2 case. We have bosses with very limited movesets and fights that don't use the environment in such a elegant manner the way Demon's did you Tower of Latria and Maneaters. In DS2, you have fights like the Giant that I mentioned, which sincerely is a joke. And then you have really awful stuff like Dragonriders, The Giant Frog from Shrine of Amana whose entirely moveset consists in hugging you or getting up and stomping you, and so on. The DLCs bring some needed variety to this, with great fights like Fume, Alonne, Sihn, Aava, but comparing with other vanilla souls experiences, DS2 is really barebones in this department.
On level design in DS2 specifically, for all of its shoddy areas, I'm pretty sure that it still wins over Elden Ring on average, with its empty theme park open world and copypaste crypts and mines. Even on an individual level, comparing apples to apples, Lost Bastille > Raya Lucaria, for example. Have yet to see anything as good as DS2 DLC levels in Elden Ring, though I'm still far from finishing the game.
This one I disagree completely. For my non professional tastes, Raya Lucaria is probably one of the best levels I've ever played in a 3d game, and probably the best in the souls series (or at least on top of the game, with things like Tower of Latria being close). For much as Eleum Loyce brings a very fresh experience and a great, intricate level design that DS2 didn't have before, I think it's even unfair to compare it with Raya, not to mention Bastille.
Also, I'll read your thoughts on DS3 in a bit!