Lately for video game company's it seems like there has been a bigger focus on renewing old games, rather than trying to bring out new games. And why not? It's a good way to get the older gaming audience back into gaming on newer consoles, so perhaps, they will end up buying new games as well. For some of us, though, there are reasons we put down the old game to begin with, that no amount of updating can fix. While sometimes the nostalgia of old games feels nice, sometimes the updates just don't feel up to par on certain circumstances while playing.
Some games feel like it's only the graphics that have been remastered, while nothing has been touched to change gameplay. Because of this most remakes don't feel fresh and new, and can still run into some of the old problems that the old game would experience (A good example of this is in the Shadow of the Colossus remakes. Just before the third boss there is a leap that sometimes makes completing the game impossible, and making the jump easier in the remake would have made the game ten times better.). While updating the graphics is much welcomed in older games like Halo and Halo 2, I also feel that sometimes the graphics aren't updated quite enough as they should be. That being said, I prefer completely remade games to those that are just remastered for your new console.
Still, they can be worth buying if your old disk is scratched beyond use or has been traded in years ago, just know that you're basically getting the exact same gameplay experience now as you did back then (which, isn't necessarily a bad thing.)
Even still, there are some remakes that start to feel more like remasters after a while, putting nothing new into the experience of playing an old game. These games, though, can be a good play for people who have never played the game before, though I do no recommend them to old time fans. In most cases, if you still own the old game, and it still works, that old game is just as exciting as the new remastered or remade version, if not more so. I definitely prefer playing my old Pokemon Ruby to playing the new Omega version, despite all the changes made and new pokemon added. All that being said, I ultimately think that both remakes and remasters are typically for those of us who want to experience the old gameplay we had back when the game was first released, but they're better for people who never got the opportunity to play the game when it first came out.