Forward versus backward numerical simulations in population genetics
Your intuitions all seem correct. Coalescent simulation should be faster, because you don't track the entire population history over all t generations as you do in the forward simulation. Rather, as you work backwards in time you are tracking a smaller and small population. And with coalescent simulations it is probably very hard to incorporate the full range of evolutionary processes whereas doing so is more or less trivial with forward simulations. 

A 2008 paper by Carvajal-Rodriguez reviews some of the issues in more detail that I have here.