I haven't played GX or XGRA, but I have played AX and XG3, so i guess I'll just make my assumptions on that, since AX is similar to GX.
I played XG3, and i really liked the sleek, neon futuristic environments they had for it. I dunno. It was just cool. But it was also slow. Cause anytime you wanted to go fast, you would just bash into the wall when you came to a corner, and that's another thign about it, the handling. OMG. You couldn't do a tight turn if your life depended on it, even with the airbrakes. And since turning was a major problem, I couldn't beat the game, so I used cheats

And because of that handling, my fave level was Muon Harbour - the very first level, cause one, you didn't bash any walls and hence maintained top speed (it was an oval track), and two, when you boosted until the speed of sound (very cool aspect), you could KEEP doing it. I also didn't like the weapons. They were more of an annoyance than a help. So i always played against my friends and in arcade mode with no weapons.
Phew.
AX, in conmparison, is FAST. If any of you have played it, you know what i mean. Just imagine this: XG3 is Mario Kart 64 in comparison. What i really like about AX is the handling, because one, it is spot on, and two, the air brakes can give you HAIRPIN turns, even moreso than F-Zero X's airbrakes. These sorta turns a re really needed, especially in the hardest and longest track of the game, Green Plant. No weapons and good handling means that you can concentrate on doing mach speeds and bashing into the opposition like we all do in F-Zero. Hehehe.
I look forward to XGRA, but I won't buy it unless i really like it, and that means a rental beforehand.
So thanks for reading my 8 cents.