You are not going to get a whole lot more out of that Integra. The auto trans is a major reason (as is its gearing, as Ecky already stated). Maybe you'll be able to put some distance between it and the Buick in terms of FE once the neglected work on the Integra gets done. Further improvements would be possible in the Integra because you can use its OBD2 port for a ScanGauge or UltraGauge to monitor your driving with greater precision than I think an MPGuino can offer.
But none of that matters if the Integra has been so neglected that it costs you real money in repairs in a short while. Given what you describe in oil, spark plugs, and cables, I would wonder if the AT fluid has ever been changed.
And that Park Avenue is so 80s!
Go with the Buick.