Whatever you do, stay away from NiMH rechargeables - they just don't cut it.
I've not fully tested battery life with any 9v batt, but I've had downright poor experiences with regular old Duracells / Energizers. I seem to have picked up multiple bad batches that have had little to no capacity left straight out of the box.

FWIW, I've had success with Energizer e2's. Haven't tried the higher grade Duracells. And I have no experience with lithiums. Not a lot of help, I know, but there it is.

Now you have me motivated - I'm testing the e2's I just got and used for a recent Del McCoury show. Will report back once I know more.
One thing that freaked me out at first - the Sax manual says:
QuoteAfter 2 to 3 seconds, the "ON" led at the center of the front panel will flash every 3 seconds.
My unit at normal operating voltage seems to flash closer to every 1.5 - 2 seconds, which made me think I'd hit the low batt warning:
QuoteThe "ON" led will flash every second when the total battery voltage drops to 14 volts.
And IME mine blinks faster than 1/sec when it hits the low batt warning.