I own the 3iX in its standard configuration, and have had a chance to hear the ModWright. I was considering both of these products at one time and was torn, but I got a great price on the BAT and have not looked back.
First, if your looking for the really warm and "tubey" sound look elsewhere as both of these pre-amps strive for neutral sonic signatures. Each has a low noise floor able to retrieve all the details like the good SS stuff but offer just a hint of tube magic that you may prefer.
The BAT does give you the option of upgrades and internal phono stage IF you feel the need. I think ModWright may be working on some upgrades and a stand alone phono stage. The BAT gets the nod for inputs, flexibility and upgrade path.
Having also owned MF gear in the past I think you will find either of these pre-amps a significant sonic upgrade. For newer tubed pre-amps I think you are looking at two of the best in this price range.