2gb is a very small environment. 2012 has a lot more functionality built in than 2000 does. It's entirely possible that 2000 runs faster in such a tiny environment as compared to 2012.

But that's a guess. It could be differences in the execution plans caused by differences in statistics or just in differences in the optimizer and how it resolves your queries. It could be different levels of blocking or contention for resources on the servers. It could be a whole slew of other things. I'd lean towards issues with memory or, stats or the optimizer.