As you've probably gleaned, a dedicated mash tun holds the grains and you ultimately pass the water through it, whilst with pure BAIB its the opposite - the water more or less stays put and its the grains you put in then take out again.
The former is easier if you have big heavy grain bills (and no hoist), the latter is better if you have limited space or budget as you just need one vessel, alebeit quite a big one (as, if done with no topping up, you need space for all the grain and all the water at once).
The other main difference is in sparging; with a dedicated mash tun you have more options, and so would normally mash with a relatively small amount of liquid and subsequently rinse through the grains with fresh clean water afterwards either continuously (fly sparging) or in batches (batch sparging). With BAIB you traditionally just mash in all or most of the liquid to begin with (though some people top up or do a bit of a hybrid by improvised sparging with the grains hung over the boiler).
Personally I've done both; I find BIAB easy and convenient for small batches, and 3-vessel systems more practical for bigger batches and slightly more efficient at extracting goodness from the grains, though also easier to get something wrong (especially in fly sparging). The run-off (whilst fly sparging) from a 3-vessel system also starts off higher gravity and reduces as you go on, so its easier if you wanted to split the runnings to make a very strong beer from the early ones, or a small beer from the latter ones, but its not something i do all that often.
Cheers
Kev
