Every author's approach is different. My preference goes to Gambit's textures, which in my opinion closely retain the original spirit. Anton's textures are pleasant, some places are great while others are a bit distracting in terms of colours or texture choice.
Technically speaking, JC's work is breathtaking. Textures are of great quality (although much too dark for me) but I have a major problem with them: I never felt I was playing at the original TR. They're so different that it looks more like a custom level than a TR1 retexturing.
I understand that was JC's decision from the start and I respect this, which is why he shouldn't change a thing about it. Many places are jaw-dropping and I was like "wow, amazing!" while exploring -- but at the same time, I was feeling totally disoriented and not really satisfied in the end. Some people will enjoy the change; I for myself am looking for a more authentic feel, which is why I prefer Gambit's take on it.
But whatever their respective style, everyone's been doing an impressive job!