NOTE: R80G/S 1986 monolevers have NO driveshaft or final drive problems - easily the best of all Gs series. They do have other problems though; gearbox is good for 70-80,000 miles, then needs new bearings, and the electrics are shaky. Rotors, diode boards, and regulators fail with some regularity. All can be upgraded with quality stuff available from Motorrad Elektrik. See their ad on our sponsors page
You will also need to beef up the rear subframe considerably. See Ernie for that - yes another sponsor - his ad is at the top of all HUBB pages.
Other than that, the G/S is a good bike, ours worked well on our RTW.
The 1100GS is a very different bike, but well-proven, very comfortable and capable for two-up round the world stuff. They do need a couple of tweaks for sure - see the Touratech ad at the top of the page and look up their "hard parts" for the 1100GS - REQUIRED fitment for all 1100GS's!
If you're comfortable doing your own repairs and maintenance the G/S is a great choice - if not, go for the 1100. The G/S will probably need more, but you can fix it yourself. The 1100 should need less repairs (AFTER it's been gone over thoroughly by a pro mechanic who understands what you want to do and fixes what's needed) so will probably be a better choice for the mechanically challenged.
No matter which one you get, you WILL need to spend some money on a thorough service, some new bits, tires etc. Budget £500 at least for that, possibly more.
See out story on our rtw trip for more on our G/S, and read the travellers stories and "which bike" forum for more on both.
Hope that helps.
Seek, and ye shall find.
One world, Two wheels.