I played the remakes back when they came out and I have to say that they were some of the best remakes I've seen. For anyone thinking about getting it, you should know its extremely hard. The original games were extremely hard as well. These three aren't games you can rush through like most platforming games. They're faithful to the source material. Just better quality. If you haven't played Crash Bandicoot before, this is a wonderful place to start. But I wouldn't go into it thinking it'll be a platformer like Mario or Sonic.
That being said, these are wonderful games to play. Be prepared to get angry and I'd suggest to have a game in mind for a break. Its a good game to get kids, but it's probably better to buy it for someone who is more skilled at games. It's also a perfect present for someone who finds their current games too easy.
The controls worked well for me and i didn't notice any lag. It was hard and i did get angry, but i grew up with a complete collection of all the Crash games so i was perfectly prepared for what I was getting myself into.