Depending on which TR6 box you are looking at, the longer TR3 input shaft will not mesh properly with the other gears. I forget the change point offhand, but that was the case with the TR6 box I put in TS39781LO. However, the shorter shaft (and a new pilot bushing) seemed to work just fine for me.
Pre-50K TR3/A will require some massaging of the transmission tunnel to clear the starter bulge. You'll also lose that nifty dipstick (unless you rebuild the TR3 top cover to fit the TR6 box as I did). Swapping gearshifts may be a problem if you keep the TR6 cover as some of them used threaded pins instead of the through-bolt, but you could probably drill for the bolt.
Again depending on the vintage of TR6, you may need to replace the 3 studs between the engine block and gearbox. The gearbox front flange got thicker over the years, requiring longer studs.
If you are keeping a TR3 clutch, you might want to swap over the longer TR3 front cover. I eventually went to a 4A clutch & shorter front cover which worked fine for me, but it seems a lot of TR6 folk have problems with that short cover so I'd keep the old one with the old clutch.
As noted, the TR6 trans does have synchromesh in 1st gear, plus a slightly higher ratio (which makes it much more useful IMO unless of course you are pulling stumps
) You will have to elongate (or just drill new ones that touch the old ones) the holes in the rear crossmember, where the motor mount bolts to it.
Late TR6 will have the wrong speedometer drive gear. Don't know offhand if the TR3 gear will fit and be correct or not (I used a TR4 OD which neatly ducked the problem).
There are also some good rebuild articles on the VTR site :
https://www.vtr.org/maintain-index.shtml
(scroll down for links)
Not too difficult, but you'll probably want to make some of the tools required and buy a few others. Don't forget to use a new mainshaft circlip every time you install it ... I'd suggest buying a few spares in case you don't get it back together just right the first time.
Also be sure to check ALL the clearances ... don't assume that new parts fit correctly. In particular, there seem to be a lot of mainshaft gear bushings that don't fit properly ... on my last rebuild I wound up having to shorten a gear slightly and use a larger spacer washer because the new bushings were not long enough.
Personal preference : I don't like the narrow steel bushings that the TR6 used for the clutch cross-shaft to ride in. So I converted to the wide brass bushings from a TR3 (two of the RH bushing without the slot for the lock bolt) and added grease zerks for them.
Don't forget to add the taper pin reinforcement, and make sure the locating dowels are in place.