I think your concern is the response time...(per your message's subject)
Generally, DC's response time is not quite good. It's really hard for me to take my son's pictures as he'll not stand too long and let you take a picture... so, that's why I choose DSLR at that time.
However, it's quite heavy (while compare with DC) and the price is higher. DC is all in one... (with len)... if you use DSLR, you may need to buy extra lens later.
I recommend Canon, response is faster, picture is sharper and good exposure. I am now using Canon IXUS 400, it is small too. It's good enough to print 8R size photo. But it can't use 3A battery and the flash is not so powerful. New model is Canon IXUS 500 with 500 mega pixels.