First one of my pet peeves, it's Randy Rhoads not Rhodes. Second, I don't like tune-o-matics. I like the string-through fender fixed bridge style like on american hardtail strats. It doesn't fall of without strings, it can accomedate every fretboard radius. If your RR is a jackson it's probably 16" while TOMs only come in 12". And you don't have to recess it or change the neck angle. Also it has a wider intonation adjustment range. Usually TOMs are not recessed so the strings on a gibson are further of the body as on fenders, I like my strings closer to the body. So that's what I would go with. If you do, go with the one with 3 screws under the saddles. There are aftermarkt ones with screws on the corners, but that's a stupid design.