The difference between compact digital cameras and the smaller DSLR's is huge. Compact digital cameras will do o.k. at base ISO in bright outdoor conditions, but will be miserable for all other purposes. Even when used under optimal conditions, you would wince at the difference between any of them and a compact DSLR.
All compact digitals entail serious compromises and there's simply no clear winner. If you must still use one, you will have to do your own research as to which one best suits your needs. Start with the Canon models, though. Perhaps look at Fuji too. Some, like the previous gentleman, will say that the Canon G9 is the best of the bunch, and that's probably true, but it's rather large and heavy and its results are still far inferior to, say, a Nikon D40x. The Sigma DP1 sounded promising, but that's been vaporware for over a year now.
Good luck.