The remote box are from earlier minis, I think first designed by John Cooper. When BMC was taken over by Leyland they decided to produce the rod change as it was easier and cheaper to produce. Deluxe's came with 3 synchro remote box (1st gear doesn't have a synchro, I have one of these for sale in the For Sale section

) and the mini K came and Cooper S's came with 4 synchro remote boxes.
IMO the remote boxes have more advantages over rodchange. The gearchange is much "tighter" than rod boxes, but you can get the rod box to be quite tight with some adjustments. The engine steady issue is no existant with remote change. I still prefer a remote box after having driven one.
Probably the biggest disadvantage of remote boxes is the fact that the parts are harder to come by and some parts are just not available new.
Just to let you know, the main reason that I am doing up this 1275 engine with remote box to replace Lillee's (perfectly good) 1098 is because it's currently a rod change box! I am sick of it! the slack is too much and I couldn't be bothered to change the parts necessary to tighten it up. It feels like a chopstick in a empty cup at the moment
