For what it's worth, you can probably turn an airbus with ULD's around faster than a B737 - since the aisle is slightly wider, which means that boarding is faster and ULD's can be on the aircraft within about 10 minutes of coming on stand. Both can be done as quickly as an airline might realistically want to do it, though - 1 min per 6 seats, if the cabin isn't completely trashed? Also, you don't have to put bags in containers on airbuses.
The B737 family and the A320 family are targeted at a pretty similar market. It's just that the A320 family is about 20 years younger than the B737. The Airbus is more economical, faster, more efficient, probably as well adapted to quick turnarounds and multiple sectors. But they are newer and more expensive; they are less abundant and more expensive.
I am pretty sure that it's fundamentally a cash-flow issue, rather than any operational one.