Sphinxes are a variety of magical beasts, the various kinds sharing little except for a general winged quadruped shape that comes with Pounce and Rake abilities. The initial MM describes four subspecies.
12 magical beast HD, large size, good land and fly speeds, and great ability scores (at least +6 everywhere but in dexterity) mean we're off to a great start. The lack of natural attacks beyond two semi-neat claws is disappointing, but pounce and rake make up for that. +13 natural armor doesn't hurt either.
An androsphinx signature ability is its Roar, which can be used thrice per day and grows stronger the more often it's used in a particular encounter. The fact that it's non-friendly doesn't help, though, and the fact that it takes multiple rounds to optimally use is terrible.
Finally, androsphinxes get a small amount of cleric casting. 3rd-level spells at ECL 12 are somewhat lacking, though.
What LA to give? Compared to something like the lammasu, another flying, pouncing, magical beast that gets cleric spells (and ended up being assigned +2), I think +0 LA could be justified. The chassis is nice, but it's expensive for what's basically a gestalt fighter/adept.
10 RHD, with about everything inferior to the androsphinx otherwise. No casting, weaker claws, no roar, lower speed... A well-built tier 4 or 5 could blow this out of the water with ease, if only by being able to use weapons. Pounce and high strength are neat, but not when they cost half your build. -0 LA.
8 RHD, but a chassis that's far superior to the criosphinx's and actual racial traits. Lots of SLAs, some of which aren't even available to full casters at this point, and a permanent Glyph that can be changed once per week. All of this comes with a chassis that's still got large size, pounce, and +8 strength, so it's worth a +1 in my book (arguably even a +2, in fact).
Hawk-headed sphinxes this time. 9 RHD and a very fast fly speed, but once more nothing truly worth spending nine levels on. -0 LA.