I live at the Enclave now until the end of J-school. My first time through LR, E-school, my family and I stayed on base in the privatized housing.
I wouldn't stay at the Enclave long term. The Enclave is nice, but not for long. The building is falling apart; it was poorly and quickly built. There are cracks developing in the foundations/floors, the pools are on the first floor - stalactites are forming in the parking garage underneath them.
The administration isn't efficient or responsive sometimes. Granted they are new and working out the administration wrinkles. I had to take my family to a motel for the weekend after the Enclave wouldn't let in Dixie Furniture Rents while I was still in Germany. The Enclave had my verbal permission for Dixie Rents to enter, but refused. Soon after the Enclave developed a written entry permission form.
The location is great, north of downtown across the river (10 min walk across a pedestrian-only bridge), next to the ballpark, riverfront running/biking trail, farmers market, Cregeen's Irish Bar...the list goes on.
The privatized base housing was great too. Though I had a different house than most PIQ/PXA guys. We stayed in a larger, free standing house off California Ave near the big base lake. My wife was to deliver shortly after we moved in and two grandmothers were staying with us. Several friends had smaller duplexes.
Overall both places are nice and have pros and cons. I expect to pay more out-of-pocket for the Enclave than base housing, about $1K, but knew that moving in. Power, water, trash, cable TV, internet, and phone aren't included at the Enclave, they were for me on base in 2007/08. The drive is much shorter on base and saved about an hour each day, not to mention morning front gate traffic. Though the base didn't have as many cultural attractions nearby as the Enclave does.
PM with any questions on either.
Oh, both accept pets and have referral bonuses.