Probably the Mini w/ SSD since it's a quad core and none of what you mentioned will tax the GPU much (the HD5000 is better than the HD4000 so that's the only real advantage of the MBA). The SSD will also be faster in the MBA, but even comparing the relatively slow SSD in my 2011 to the super fast SSD in 2013, I really don't "feel" much of a difference in day to day activities.
Having both a Maxed out MBA (okay sans the SSD as I only have a 256GB SSD) and the Mid-Mini w/ SSD I think I'm a pretty good judge of what is "better"....
Now, will either computer do? My guess is yes. The i7 in the MBA is still a pretty decent processor (even with just two cores), so I don't think either will be a problem. The 8GB of RAM MIGHT be a limiter in the MBA, but I am still able to do quite a bit even running a VM on my MBA, so.....
Ultimately if you don't need portability then I would just go with the Mini.