We hired a 140 DSG conversion last summer and went cycling in the Alps. That's three people and two bikes. No problem getting up anything, including Col du Glandon and Alpe D'Huez and Col du Telegraph. Admittedly that's not as steep as some climbs, such as in the Pyrenees, but I really wouldn't worry.
I've now bought a new 140 DSG California, which might be slightly heavier since it's got a bigger water tank (though you don't have to fill it, or even have anything in it). The 140 is a simpler engine and cheaper to service.
I didn't even use Sport mode then but I've since seen lots of people recommend that for hills. The DSG is actually very good at dropping down through the gears when needed.
All in all the 140 is definitely sufficient as long distance tourer/cruiser. But it's no sports car.
One point worth mentioning: the 180 does have bigger brake disks I believe, that's why it comes with 17" wheels. After descending the Alpe D'Huez the 140 did have a lot of 'hot brake' smell. Perhaps the larger brakes would have helped. The Sports mode would have too as it gives more engine braking. If you are doing a lot in the mountains I'd be more concerned about overheating brakes on the way down than lacking power on the way up. We just stopped from time to time to admire the view instead.