Hi Duncan,
I'm sure that you and Garry are speaking as you find.
So am I..!
I've definitely noticed the damping effect of carbon fibre when I've been able to use CF tripods.
That, and almost 30 years' intimate experience of the stuff as used in fishing rods, leaves me in no doubt that -
all other things being equal (and there's the rub) - it will handle unwanted vibration better than aluminium.
A "heavy" aluminium tripod will be more resistant to large
movements than a light CF tripod, and I've no doubt that a similarly heavy/similarly designed CF tripod would give the metal one a run for its money in the same situation.
But I'm talking about high frequency vibration of the kind that will blur a photo without you being aware that it's happening (I intentionally never mentioned wind-induced movment) - carbon is
significantly better at dealing with that than aluminium.
Aside from weight-saving, one of the main reasons CF is used for fishing rods is that it quickly damps out vibration of the rod tip on the cast, thereby increasing casting accuracy and distance (this has rarely mattered to me, but competition casters say it does matter, and I believe them).
Likewise (and this might have some resonance for you, Duncan!

) bike frames made from CF were initally introduced
specifically because of the damping ability of the material.
So - while it's hard to prove definitively outside of a laboratory - I'll take some convincing that given two otherwise similar tripods (similar weight, design, height) side by side, one in aluminium and one in carbon fibre, the CF one won't be better
damped.
Not necessarily "more stable", which I believe is mainly down to the mass and the design of the tripod (and which therefore could also be something a CF tripod could deliver - how wide the legs are splayed being
massively influential there, I'd have thought), but there's no question to me that damping is CF's forte.
I also acknowledge unreservedly that for most people it might be an utter irrelevance!
There's still a significant market for tripods made of wood, I notice: their main selling point is also stability over and above metal tripods - Ries for example say:
VIBRATION - A metal tripod will pick up vibrations, amplify them, and transfer them directly to your camera. The most expensive photographic optics can be instantly rendered worthless by these tremors. RIES tripods, made of wood, absorb the vibrations, and provide a stable and vibration-free support for your camera.
Berlebach reckon:
Berlebach ash wood tripods are low-vibration products.
Ash wood is capable of compensating for the shudders and vibrations that constantly occur in the working environment. It will ensure that you get exceptional results with your camera or your sensitive optical or measuring equipment.
Properly used, carbon fibre will deliver the same benefits. A
badly designed carbon fibre tripod would be the worst of all worlds though, without doubt.
And I've
got to disagree with Garry's observation that Manfrotto tripods aren't durable... unless they're being used in a war zone as a mount for a rocket launcher, they'll last as long as you like and - importantly - spares are readily available.
James, how tall are you?
I ask because - being vertically challenged myself at 5' 8" - I've found the 190 series more than enough (and equally usable by a 6 foot tall bloke I used to bird with), and they're a wee bit lighter for the same level of performance. They just don't go quite as high as the 055s.
If your Leica is an angled scope, you really should consider the 190 range too.