It really depends on the game in question. I've enjoyed a couple of remastered games such as Shadow of the Colossus and the Devil May Cry HD collection since it gives me a chance to experience an older game I never had the chance to play on its native platform and arguably in the best way possible on a modern platform. That being said, price is also another factor. I'd flat out refuse to pay more than half the price of a new release.
Speaking as someone who's only dabbled in the original Devil May Cry, never played DMC2, and played the shit out of DMC3, DmC is a really interesting take on the source material. Like you, I really dug it despite being one of the many fans who had an immediate knee-jerk reaction to the Dante redesign. Most of the differences have been covered by other posts in this thread but if you liked DmC there's no reason you shouldn't like Devil May Cry 3 at least.
Been eyeing up the God of War Collection (GoW 1 & 2 HD) and God of War 3 since I've never played any game in the franchise and feel like I should after getting a PS3 this Christmas. However, I'm not entirely sure where to start. Thoughts?