OK, so I have a Macbook Air 11"

Sounds like your current setup is sufficient. If you need more power (need details) and you won't miss the portability, get the mini. I feel the iMacs have lots of power but may have problems after heavy use due to insufficient heat dissipation.

I did the opposite, traded my base mini with 8gb of ram and my monitor for a i7 11 inch air 4gb/128gb. Now looking for a thunderbolt display.

I dont think you get much performance difference between the two when looking at the base model. If anything the air is slightly faster. I did lose my 8gb of ram + 512vram which lowered my framerates in CounterStrike when using an external monitor but playing on the laptops native res is fine. As far as only having 4gb compared to 8gb in normal usage I haven't noticed any slow downs especially because of the SSD.

I guess it depends on which mini you are thinking of buying. If its the server and you need the quad core then sure the performance difference is alot but if its the base model and mid you don't gain or lose anything (if anything you lose value because desktops are alot harder to sell and command a lesser price.). You do get a discrete gpu with the mid model so you can take that as a gain if you game.

wondering the same here. Made a major mistake by getting the 11'' Air with just 2GB RAM in 2010 and it is getting slow.
But as I have the 24'' ACD, keyboard and trackpad, the Mini could be an option, with 8GB RAM and SSD. Depending on how expensive that will be.