Ugh, ok. To both above, no.
The RR24 did not exist when Alexi was with Jackson. They made it afterwards, and they are very similar. Main difference is that his (aside from being custom shop) had gold hardware (OFR) and white binding on the neck as well as MOP inlays and a white logo.
And Nase, you can't compare the RR24 with the 200, they're on totally different levels of quality. You'd have to compare it with the 600.
I currently own a RR24 (ltd. model) and an ESP SV, and having played the 600, I have to say I prefer the ESP's. But that's just me. There really is no "better", only what you like more.
The ESP (LTD) will have a bigger body, but better fret access. The tones will be very similar, considering the comparable build quality and exact same wood choices (alder body, maple neck, ebony fretboard).
However, the ESP will have a passive EMG, and the RR24 will have the active 81. But that's honestly one of the easiest things to change, so I wouldn't base it on that. Plus, the ESP will (probably) come with the MM04. I'm basing this off of his new signature EMG, which I'm pretty sure will come in his new ESP's.
Choose which one feels and sounds better to you. They're both great. I prefer ESP, personally.