>>makira+(OP)
I think it is very intuitive that more space beats the pants off of more time.
In time O(n) you can use O(n) cells on a tape, but there are O(2^n) possible configurations of symbols on a tape of length n (for an alphabet with 2 symbols), so you can do so much more with n space than with n time.
>>LPisGo+Y9
I think it really depends on the task at hand, and not that intuitive. At some point accessing the memory might be slower than repeating the computation, especially when the storage is slow.