Jesper Kyd would definitely make it sound a lot more like Hitman. I also miss the old fiber wire system. There are a number of differences but I think the game still has the same design philosophy for the most part.
Absolution took the series in a legitimately different direction that a lot of fans did not want. This new game feels like Hitman in terms of how levels are laid out, how you take out targets, etc. It plays quite a bit differently and that's because every single control has been changed. There's a run button, a cover system with its own button, a button dedicated to Instinct, dragging bodies looks and feels different, etc. At a mechanical level, the game is wildly different which naturally makes it feel different.
From a game philosophy/design angle, it's rather faithful to take her series at large. The change in disguise systems and how enemies react to you isn't a stretch. The game has always changed how guards behave, how aggressive they are toward you, and even how disguises work. C47 is much different experience than later games which all share a similar feel but have a number of notable and important differences. SA's disguise system is rather unforgiving and forces you to walk around most people otherwise you arouse suspicion and you have to keep your distance usually. Compare that to BM in which you're free to run around and circle around guards over and over with next to no consequences. That right there immediately makes those two games pretty significantly different when it comes to how one engages with the game.
I feel as though the new game is the same, the only difference is, as said, the last Hitman game that had the same game design philosophy was BM back in 06 and was available on PS2 and Original Xbox if I'm not mistaken. That's a huge gap between it and the new game and games have changed a lot. I don't think fiber wiring someone and immediately dragging their body is bad, it's just more convenient than old games. However, I do think the one button, instant fiber wire does fundamentally change the feeling of it. I would have loved the best of both worlds -- hold the button to ready the wire and get it taut, release to strangle the person, immediately goes into dragging the body. Would have been great. Since the wire is iconic and so important, it would make sense to make us feel like we're actually using it by holding the button. The lack of a sniper briefcase changes how sniper rifles work. These are all changes that affect how the game feels just like all the other things including a different control scheme.
But! Things like exploring the environment, listening to conversations, finding poison or other weapons or innocuous items that can help you without knowing why or how they necessarily work feels like the old games IMO. It's not perfect. It by no means feels like a direct sequel to Silent Assassin or Blood Money and the difference between it and BM is of course more pronounced than the change between SA and BM. But again, it's also been a lot longer since BM than SA was to BM.
Not giving you a hard time or anything. There are a lot of ways it feels different mechanically but some things can be made to feel more like the old games. Playing on Professional mode with only one save can introduce a lot more stress. Cameras work more like cameras by sending guards to investigate if they caught you trespassing on camera or doing any sort of illegal action, you can turn off the mini-map and Instincts and Objectives and Opportunities and Challenges so you have to play pretty much blind going in. Me? I don't like Instincts but miss the old map so I keep the minimap on. Pros and cons -- the old map was omniscient and allowed you to see everyone, everywhere, on the map, regardless of what level they were on but you had to stop and use it. The minimap is real-time and available at any time since it's in the corner but it also only shows what's directly around you and doesn't really help locate your target from across the map. But if that's still too much, they allowed us to disable it.
Anyway, I hope that makes sense. Mechanically it undoubtedly feels different as every little thing has a different control and you can't go first person. But things like the new disguise system to me don't feel too different from the old games because all the old games already had different disguise systems from the much tougher SA to the very forgiving BM. This is just yet another disguise system and one that thankfully allows disguises to still make sense and work unlike Absolution which pretty much ruined how disguises work IMO. But in terms of the game design philosophy behind the game, it's still in line with Hitman IMO. Again, not perfect but yeah.
TLDR: At a mechanical level (i.e. fiber wire, controls, cover system etc.) it feels completely different. At a game design philosophy level (i.e. exploring sandboxes, assassinating targets, sometimes other types of objectives, finding weapons or gadgets or seemingly innocuous items that can help in assassinations, accidentso, etc.), it's got the same sort of ideas and philosophy as the old games with some changes here and there. I can't tell you how to feel nor would I want to. You don't get the same feeling and that's fair enough. I just wanted to mention why I get a similar feeling if not the same exact feeling as the old games and why I think some of the difference in feeling is there.