That's been a popular pairing, I'm thinking Space House needs to happen in the future. I've had more than a couple requests for both in the same box.
Space house would be awesome!
The biggest difference between the two is where the tone stack comes in the circuit.
PA: input -> first stage -> tone stack -> gain control -> second stage -> master volume -> output
LU: input -> first stage -> gain control -> second stage -> tone stack -> master volume -> output
Tone stacks are inherently lossy, they're going to drop the gain a little. LU bites a little harder than PA because it keeps more of the first stage gain that can go on to hit the second stage, so you have two full stages of gain before it hits the tone stack, whereas the PA loses a little gain after the first stage in the tone stack so it doesn't slam the second stage as hard. Neither is right/wrong/better/worse, they're just different.
Outside of that the differences are minimal, to the point I've thought about combining what I consider to be the best points of both into one pedal so I could cut down on the number of models I offer, but I don't know that it will ever happen.
Though that is more or less what Space Heater is, I took my favorite aspects of PA and favorite aspects of LU, dropped the tone stack, and put it in a little box.