I looked at a Luggie - it's much heavier, at 50lb plus battery at 3lb (although I find that battery weigh hard to believe)
The Travelscoot is 29lb, with a 6lb battery. Range is 12 miles, speed is 6mph. Travelscoot is the only one that is approved for carry on on airlines, so you can ride right up to the aircraft steps (not that I'm well enough to travel anywhere).
If the Luggie's battery is only 3lb, I doubt its range (quoted as 12 miles as well). But I do think that figure is wrong. It is also slower at 4mph, and more expensive.
I keep the seat assembly whole, so the thing is just 2 parts plus the battery. It fixes in place with a quick release lever, which is easy to do up and undo. You do have to remove the battery and seat assembly to fold the trike, but if you had a big boot, the handlebar collapses telescopically, so it might fit whole.
It really depends what you want to do with it. I don't have room here to house a Luggie without carrying it upstairs. The Travelscoot main frame is small enough to leave downstairs without annoying anybody. I like being quick, and being able to pick the whole thing up with one hand means you don't get stopped by obstacles. I'm allowed on the buses round here, but I doubt I would be on a Luggie.
However, the Luggie is more of a 'proper' scooter.