Dark Souls 3 is by far the best Souls game Fromsoft ever released, whether it's in the gameplay, world design, PVP, Bosses or even the OSTs. I heavily recommend people to play this game first more than any other Fromsoft game.

(Just a heads-up, I'll heavily compare DS3 to DS1).
Starting Area (Tutorial)
DS3's starting area compared to DS1's starting area is laughable, whether it was the design of the area or the tutorial boss that's in it. Iudex Gundyr as a tutorial boss works perfect with the way DS3 is, since you have different gameplay mechanics such as: Parrying, Magic, Pyromancies and Melee. Gundyr unlike DS1's tutorial boss (Asylum Demon) you can use the Parry system against him, something that DS1 doesn't use on any of it's bosses (only the last one, but you probably going to 3 shot him any way), also Gundyr has a second phase something that Asylum Demon doesn't have and not to forget that Asylum Demon's attacks are really slow/easy to read and has limited attacks/combos. Where Gundyr in the other hand as a tutorial boss has lots of different attacks even in phase two his attacks change and so does his form. Lets not forget the OST! Gundyr's OST is very good to listen to unlike Asylum Demon's OST, I'm 100% sure no one listens to that.

Something that I didn't like about DS1's firelink shrine is that sometimes the Firekeeper sometimes disappears/died and need to bring her back, for me it was such hassle and annoying. In DS3 that doesn't happen thankfully.


Bosses


Bosses on DS3 compared to DS1 is way faster; because now bosses are actually difficult and somewhat difficult to read their move set until you get used to them where in DS1 you can just kill most of its bosses with ease first try; because of how slow they are and easily predict their move sets (except for Stray Demon fuck him). Something that I've always wanted to know about DS1 is, what's even the point of the parry mechanic if there's only one boss that you can use it on (it's the final boss) where in DS3 there are a total of 6 bosses that you can parry and they're scattered through start-mid-late game. Another thing that I've liked about DS3's bosses is the OST! I loved every single OST the bosses have on DS3 (except for the Curse-Rotted Greatwood Tree boss, fuck that OST) other than that all OSTs are very good and let's not forget the DLC bosses in DS3 they're very good and have top OSTs. Oh, not to forget the bosses on DS3 are hard but that doesn't mean they're not balanced.No, they are balanced and there are no RNG based bosses (Fuck you The Bed of Chaos from DS1) and they're all fair to go against.
Just compare some of the early bosses to DS1's bosses most of the time you'll love DS3's bosses more; because they're more fun to go against and there's actual challenge on fighting them and not just some crappy boss with dumb pathetic attacks. Here it's more challenging and more fun. I want you to also compare the final boss of each game, you'll see that Soul of Cinder is 10x harder than Gwyn in DS1, Gwyn isn't even that hard of a boss to kill too and you'll probably kill him before even seeing all of his attacks.


Gameplay


Gameplay on DS3 is same as DS1 but faster and more difficult, difficult like it's now harder to parry unlike in DS1 and also now you have Mana stats that gets consumed when you use Weapon Art Attacks or Using Magic attacks. It has its own flask, so now you have to balance between Estus Flask and Ashen Estus Flask. One used for healing and other to regenerate Mana. There are lots of parry able bosses too as mentioned before. Playing with friends is also fun or getting invaded by randoms never gets old and always good to have/get. Sadly, same as DS1 Magic is boring to use/do unlike how it is in Elden Ring so don't expect much from it and Pyromancy of having fun.


World Design and Progression

The World Design and Progression is a lot different from each game, but I'll just say my personal opinion. Personally, I see that DS3's world progression is better than DS1's progression; because no matter how you see it or how connected the world of DS1 is, you can't tell me that I have to backtrack from fricking BlightTown to Firelink Shrine and there are no warps until you get to Gwyn's daughter, this...is a hassle and very annoying. In DS3 however you get the warp system immediately and can travel to every single bonfire unlike in DS1 not all can be warped. Yes, the world is not connected in any way, but I really do not care as long as I can play without knowing I have to backtrack and get annoyed.


DLCs

DS3's DLCs are better, also DS1's DLC is better than the main itself.DS3's DLCs are worth to get trust me, a lot of rememberable bosses are from the DLCs too Slave Knight Gael (The Goat), Twin Demons, Midir and Sister Freide are all bosses that are challenging to fight and very fun to go against. I highly recommend having the DLCs in your first playthrough.


In summary DS3 is a very good game in all meaning and enjoyable with the vast majority of bosses all good (except for the Rotten Wood boss) and the OSTs oh my god the OSTs I love them so much, there are also NPCs and quests you can do and covenants but meh not worth mentioning.