Depends on which type of Slipper you use.....
Old Salisbury Powerlok, Early Quaife, later Jack Knight's, and most Minispares Plate types usually require the Gearbox Casing & Diff Housing to be hacked around (sorry, modified by grinding and polishing) to enable them to be fitted, there just isn't enough space within most casings for everything...
Only the very early BMC Special Tuning/Jack Knight MK1 Cam & Pawl type LSD will definitely fit without casing modification, and these are totally obsolete, being some 45 years young!
I happen to have a couple of these VERY rare items, but I would'nt recommend using them, Driveshafts etc, being completely different..
Virtually EVERY LSD that I've ever done needed some clearance to be found, it's not difficult to do, just time consuming, helps if you have access to a Milling Machine or Lathe..
Sometimes, even the Crownwheel to Diff Bolt Heads foul on the Casings, so have to be "Thinned" down to clear. Despite what Minispares will tell you, it's not exactly a straightforward "like for like" swop, I would say that you nearly ALWAYS have to modify and alter something!
The LSD itself, together with it's special, non standard Output Shafts are all somewhat bigger in size than a Standard type Diff...
Sometimes, even the (Special) LSD Type Crownwheels are too small internally to fit properly onto the actual Diff unit itself, and these have to be modified (by grinding) to fit!
At least if you use a Crosspin/4 Pin Diff Unit, these WILL fit without modification, also means that you can use Standard type Crownwheel & Pinion, although I would only recommend the Genuine Minispares Diff.
Certainly avoid the Mini Sport ones, they tend to spit out their Roll Pins with alarming frequency...
Cost is probably the biggest factor, ANY good LSD, etc will cost you (at least) four or five times what a Standard Diff will...