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.