There are some that can do both quite well but there is always a compromise in some direction.
For travel, both Michael & I are using light weight Traveller tripods kitted out with an Acratech levelling base and a Gitzo fluid head.
The compromises here are stability, lack of easy vertical mode for stills, only 10˚ of levelling and only fair fluid head function for pans & tilts. But given those compromises, the resulting kit is small and versatile.
For video, the need for levelling and smooth pans & tilts requires the use of a proper video head and a tripod with a bowl- complete overkill for stills and lacking the easy adjustment to vertical or portrait mode.
I'd be very interested in others' experience.
Hello Chris, are you using the Gitzo 2380 or the smaller and lighter model?