The Fathom f112 has automatic room correction (D.A.R.O.) and comes with its own calibrated mic. A nice feature if you setting up your own system, especially if you are a novice with subs, but you mentioned that your dealer will be doing the set-up so you will be paying for something you will not be using.
The Paradigm has ARC (Anthem Room Correction) but I don't know if that is operational right out of the box or if you need to buy an accessory to make it work, but again if the dealer is doing the set-up, they should be able to supply the necessary tools for optimal operation.
Sound quality should not be an issue, with proper set-up, either one should sound good. The Fathom cycles 3 Hz lower than the Paradigm per their respective specs. In reality that is just going to give you a little more room shake. Is that room shake worth 6 grand? That is your call.
As it has already been mentioned, the most important part for obtaining the best sound quality will be the crossover, which you already have in your receiver/processor, make sure the dealer uses it in their set-up.