The base mechanics definitely feel different. I would argue that DS1 is the more dependable one, though. There's rarely ever the issue with hitboxes that DS2 had, for one. For another, things like parrying are much tighter, and much easier to consistently pull off. Enemies are still difficult, but it's easier to predict their moves, and thus pull off parries or whatever. (Less WTF deaths.) Compare fighting a Black Knight to a Heide Knight. The Black Knights are hard, but predictable. The Heide Knights just have a really weird moveset that's difficult to predict. That kind of thing, in my opinion, leads to more "unfair" deaths. (Not that every enemy in DS2 was like that, though. Really only a few.)
I would also argue that NOT giving you the ability to warp at the start of the game is hugely important for the design of Dark Souls 1. For one, it forced them to much more careful with their level design. (Shortcuts, area connectivity, etc.) I think the more important aspect is how it forces you to commit to your actions more. You make it to certain areas of the game and you really *feel* how far away you are from where you started. It's an almost sinking feeling of despair in certain areas, when you realize you're in an incredibly dangerous area, and getting out would be just as hard. So your only choice is forward, and the feeling of overcoming that is so good. (Whereas in DS2, it's so easy to just warp to another area when you're having even the slightest bit of trouble, and come back when you are beefier.) I feel like the level design in the second half of the game maybe fell apart a bit in part because of warping. (Pure conjecture, though.)
That being said, I love DS2 as well. It's a great game. And I'm also not a fan of the thread title, either. It seems purely motivated to be inflammatory. They are both good games, and some people prefer one over the other. Nothing wrong with liking DS2 over DS1, despite what a lot of the internet would have you think lately. (I've encountered a lot of "stop liking what I don't like" attitudes when people say they enjoy DS2.)