I spend 3 to 4 months of the year on the road, every year since the early-80's.
For the record I tour mostly 2-up.
For the last 3 years, I have been touring on 2 different bikes, a '96 BMW R1100RT and the '05 Speedmaster (and have taken both on some pretty long distances).
They both cover a broad range of uses, each in their own way.
The RT is way better for higher speeds on highways (speeds our Triumphs barely reach), right down to the not-so-tight twisties.
Built-in weather protection is also excellent (in as much as two wheels go).
Similarly, the purpose built luggage facilities are great.
Our bikes are superb from the tight twisties right up to the (what I call) high speed barrier (circa 95 mph).
Anything over that and the bigger rigs (similar to the RT) are better, hands down and in terms of power/stability, there is no comparison (and with that in mind, I agree totally with Clanrickarde's remarks) and that larger rigs (MOTORCYCLES like the RT and not HD Electra-like aircraft carriers) are definitely not overrated.
The Speedy is excellent on secondary roads and much easier to handle on really crappy roads and very tight twisties (where the RT requires a bit more planning and muscle).
Having said that, if I am to choose a bike for Western Europe and it's superb highways and secondary roads, it's the RT, without second thoughts.
If I am to choose a bike for the tighter, narrower and sometimes lousy roads of Eastern and Central Europe and some areas of the Middle East, it's the Triumph, again without second thoughts.
If I were to do a mix of regions and was ok with the lower speeds (relatively speaking) on the better highways, then, again the Triumph wins.
Edit:
Oh and about reliability and overheating issues, I have taken the Triumph to countries where they don't even have a Triumph dealer, that's how confident I am.