For a given size, a ball valve will be larger and heavier than a TOBV. Even when one orders the "Quarter-Turn Gate" valves that have the same B16.10 end-to-end as is customarty for Ball valves, there is not as much metal in a TOBV not as much machining. OTOH: the laminated seal rings commonly used in a TOBV are a tad on the expensive side to manufacture
Capacity: TOBVs have a beefy disk assembly that hangs out in the middle of the flow stream. Cv is definintely reduced. TOBVs are offered in class 600, 900, and even 1500. WHen the disk is supported by enough shaft to withstand class 1500 differential pressure, there's not really a lot of hole left with the valve open. It becomes full of large diameter shaft and beefy disk.
Ball valve can be supplied full port, with trunnion bearings that can withstand any pressure class without affecting capacity.
Torque: Ball valves have seats that are process energized at shutoff so there is breakaway Torque. Then once the valve begins to open, the seats relax a little but the ball still has to rub the sets as it rotates. TOBV valves break out of the seats and move with only bearing/packing friction. TOBV Dynamic torque is low compared to flat disk butterfly valve designs because of the offsets of the disk, but it IS necessary to lean on a TOBV's shaft mightily to get the Zero-Leakage for which they are sold. As a rule-0f-thumb estimate the TOBV would have one size larger, or slightly more expensive scotch-yoke actuator when compared to the ball valve.