If you want proof, go jump into the first level of the original game. Try dashing into new rooms as you would in the new game. Don't select an appropriate weapon or inventory item first. Don't enter in a way that you know will work best. Just run in, and once you're in the room, then adapt. It doesn't work very well, does it?
HenitoKisou: Been there done that so...
It's exactly the same to me at least. But I tried tactical approach first in original game, then in reboot with success. Also tried with no tactics and adapt and mistakes hurt the same way first in original then in reboot. With different weapons, enemies and maps adjusted to gameplay equivalent of original but because you see, hear and feel differently you play other way and doesn't notice it. I had similar problem after PK and other games or like playing SW after Blood. If environment and reality changes but gameplay/flow is intact and your way how you live/act not you feel certain fake to it. I treat reboot as same in gameplay and rest of the stuff as game on it's own and it's play exactly the same as original not because I changed the game but because I changed my paradigm, perception, to correct my reactions in same gameplay but different game reality. Game reality is predictable, simulated world, if basic gameplay is the same, your reactions is the same but everything else is not you either get used to it or blame game of feeling different in gameplay or not being faithful if it's more than engine/content reskin lol. ;-)
Yes, different people have different playstyles, but different FPSs will encourage or discourage certain things, depending on how your health works, how your weapons handle, how enemies act, what abilities you have, etc. That's why the combat in Call of Duty feels different than the combat in Painkiller. Or, the combat in Serious Sam feels different than the combat in Blood. Or the combat in Halo feels different than the combat in Call of Duty. There are differences between the new SW and the old SW. That's a fact. Differences in how the health works, how the enemies behave, what abilities you have, how you avoid damage in combat, how quickly you can eliminate enemies, the pacing of levels, etc. Whether those differences are enough to differentiate the two is a matter of opinion. You're entitled to yours, of course. But as someone with a lot of experience with all sorts of FPSs, and someone who has actually specifically compared the two games in question back-to-back, it is my opinion that the new SW is a much different game than the original.
To me, the biggest difference--or rather, most important difference--is how the player avoids taking damage. In fact, I think that's a very important part of every FPS. Because in the old one, you avoided damage mostly by acting quickly. Since a lot of enemies had hitscan weaponry, there wasn't any good way of dodging around bullets. In contrast, the new one is all about dodging. So acting quickly to eliminate threats is no longer important, and combat plays out slower, with little to no need to use cover to keep from taking damage. This is also something that sets Id Software's FPSs apart from 3d Realms' titles, in a pretty big way.
Also note that I'm not saying the new SW is a bad game, or a bad reboot. Just that it's a different sort of FPS.