If you are like me and just do a little welding now and then, a multi-process machine will take up less space and has a lower purchase price. Last year I was considering a Lincoln Square Wave 200 Tig ($1500) plus a Millermatic 211 Mig ($1200) instead of a Miller Multimatic 215 ($1800).
I chose the Multimatic 215 and have been very happy with it. So far, I have just used the mig and tig processes; and it is very quick to change between processes. It has two gas solenoids, so no need to even mess with the gas bottle connections.
As others have pointed out, it is a DC only machine, so aluminum welding is limited to mig and that would require the additional purchase of a spool gun. It is also lift start instead of high frequency which took me a while to get used to. If you do a lot of welding where schedules are critical, need to do tig welding of aluminum, or are x-raying your welds - single process machines would be the better choice.