I'm not an evolutionary expert by any means, but I don't think that the two theories you present are at odds.

Consider that random genetic mutations occur. In salad days, everything is going well, and there's not much impetus for one mutant to be better off than any other, but since the mutations are still randomly occurant, as long as they don't cause any harm, they continue happening. Then, all of a sudden, something bad happens, as it is wont to do. Suddenly, those thousands of years of mutations have something to do, and vast changes seem to happen all at once, because only one set of mutations help survive that crisis, whereas there's just been slow genetic mutation that generates a diverse population that is suddenly culled to a great extent down to only one specific population.

Just my two cents, and it's probably got a major flaw in it, anyway.