Besides being the svelte looker of the bunch (among other aesthetic differences), the Duo has a headphone jack, a stronger pcb, but more leak prone caps. The R and RX lack the jack, have shittier pcbs, yet pack more reliable caps; and the RX has the aforementioned clutch and was originally packed with a 6-button controller in place of the usual 2-buttoner.
As far as CDR compatability, methinks the R/RX tend to be more compatible due to them being slightly newer tech. There's no guarantee of any version working reliably, and the repair guys can get almost any of 'em reading CDRs (new caps, new blazing lazer, pot tuning, etc.), so it's shouldn't be a deciding factor in which version to buy.