Webers or Dellorto carbs are probably one of the best carbs you can fit to your triumph (and others). They are far more reliable than
SU/Stromberg/Solex (whatever). I expect the 'horror' shories you are hearing are from people who fittted them for the wrong reasons and just expected
them to work without setting up.
There are a few very important considerations to make here before you continue.
They are expensive to fit (even second hand ones) and you'll need to correct manifolds to fit them.
They will not give you instant power. If you do not get them set up on a rolling road you will most likely find they simply out your fuel bills up.
You absolutely MUST budget for a two hour rolling road session after you have fitted them - there are many components that can be changed to get them
spot on - this will take time.
Once they are set-up, DO NOT TOUCH THEM AGAIN! even taking them off and re-fitting them can affect them (balance)
With triple carbs, the real challenge is to balance the throttles properly and only the right equipment will do.
You will probably not see much of an improvement unless you are adding modified cams, porting the head...etc etc as well.
But the good news... with the correct set-up you should see a power figure that can match a fuel injection setup (about 99%).
However, twin HS6s would also give a good return and at the bottom end there really isn't much to choose from, when you get to the top of the rev range
though the webers will definately be better. A compromise would be a triple SU set up... this should give the best overall balance of power economy a
drive-ablility and still looks great!
Hope this helps...