I recently learned that it's possible to change the size of my embark site before starting a fortress, from the default 4x4 down to 1x1 and up to the size of the whole "Local" window, whatever that is. I'm having trouble figuring out what might be the downside of using the largest possible map. So, what is the price of getting all the extra space and resources? Do the larger borders cause more goblins/fun to spawn? Conversely, is there a good reason to use a smaller site?
The only reason to limit (or expand) the size of your embark site is due to computational limitations. Dwarf Fortress calculates a lot of stuff, and is a notorious processor hog. Frame rates creep ever downwards as you add dwarves, more mined stones, a larger creature list of dead enemies, and more fortress to path through.
If you've got a top-end computer (multi-core won't help you, as DF is single-threaded) you may be able to play on the larger embark sites with no problems (or at least until you encounter moving fluids... :P), but if you've got an aging behemoth of a machine, running Windows 98 and just chugging along... you may want a smaller embark site to cut your poor processor some slack.
The advantage of having a bigger embark is to have more resources, playable area, and to have two geographical landmarks which are far apart.
Why not make all embarks the max size? Lag, lag, and lag. larger embark means more creatures, more items on the site, more liquid movement... more everything, so, more lag.