I had a look at it on Youtube and the remaster seems to be done really well. Confirm?
Absolutely. The HD remake is just an HD upgrade of the GameCube remake that was made by Shinji Mikami himself so it's very much an upscale on all parts of the original so it retained that feel of the game, plus they re-recorded the audio of the actors and reanimated the whole thing. The HD remake itself, from what I've been told, added a DMC1 style analog control for the the stick and the D-pad retains the tank controls so you have the option of both. The graphical upgrade is all around superb with a lot of spots that look great and at worst looking decent. The CG cutscenes look rough and extrapolated, like they do on the DMCHD Collection, and just like the issues there plenty of things still retain the 3:4 screen ration, like the inventory screen, the save screen and all menus, couldn't be helped, but I guess since I put up with it in DMCHD it wasn't such a shock here, nor as noticeable. From what I've seen there is no real differences between the PS3 or 4 versions so it's about what you got or what controller you prefer.
I think, personally, that the reason why they pulled it off so well here, unlike the many flaws of the DMCHD, was because Capcom themselves made it. They took the time to be detailed and put that little extra work to replace the parts that didn't upscale gracefully and made much of it with other methods. I saw their behind the scenes for this on youtube and I saw that what they did for the game so I know they did for it. I just wish they'd done DMC in house, even if it was only one game at a time.