I played Tomb Raider Anniversary and I must say the overall gameplay experience is very different from the orginal game. There is a new save point system now compared to being able to save almost at any point in the old game.
The controls are different too. Lara can't jump high like she used to be able to, and can't back flip to higher ledges anymore or do any of the jumping sequences that included the backflip or side flip or being able to jump high. I didn't like the remake anywhere near as much as the original. It was kind of fun to see high resolution versions of the game environments, but the jumping puzzles weren't fun anymore because Lara's jumps were too limited, the enemies were not an improvement, and the save system was a nuisance (save points instead of "save anywhere"). So IMO TR Anniversary was a big disappointment. I'd read that some of the game was different, but I wasn't expecting Lara to be such a shadow of her former self.
I thought it would be interesting to give these classics a modern workover, as LucasArts did with Monkey Island.
Are you talking about the 256-color version of Secrets of Monkey Island as opposed to the 16-color version?
For the answer to the original question, I'd agree with Becky. I'd like to see The Dig made with up to date graphics. I imagine some of the game environments would be breathtaking.