I have both MIG and TIG welders in my shop, both fairly heavy duty. I have to say that, when welding up large things (even if it's thin metal), the MIG is pretty unbeatable. I made a couple of wax casting boxes out of 0.8mm steel, and the MIG did a fine job - yes, I blew a few holes, but they were easy filled, and 99% of my welds were water-tight first time out.
Where the TIG excels is, as you say, on small fiddly stuff; everything is much more controllable. The two downsides that I've encountered; it's much much slower than MIG welding - a problem if you've got 6ft of weld to do), and the amount of heat you end up putting into the work piece is immense compared to MIG - with the consequent risk of warpage. It's easier to do really nice looking welds with TIG, and of course you can go over & over a weld without constantly building it up, e.g. if you end up with a lump. Just watch out for everything getting red hod & setting your bench on fire...
When it comes to Aluminium welding, you need an AC TIG machine, and IME you need to steer clear of the cheap Chinese ones. A good Butters unit will weld well, and if you have sufficient power, a decent sized transformer machine is even better than an inverter, despite having less tunability.
Of course, the very best welding machines are up at Rob Wilson's place...