Tricky one to answer, I've heard the Denon 1910 and it's a great amp. I haven't heard the 2310, but I've read posts here from a number of people who've heard both and they all agreed the 2310 was worth the extra money. However, to be 100% sure, you ought to try and demo them first for yourself.
At the end of the day, the 2310 + speakers is over your budget, but if this is okay, it may well be worth it!