I can't really comment on the specific vehicle as I've never owned one. We did, however, tow our Jayco 1207 with a Chevy Trailblazer, that worked great. I would not want to tow a 17Z with it, even though it was within its towing capacity. The problem with smaller SUV's is that the suspension isn't really made for towing, they are fine for smaller trailers/popups, but you put something high profile back there, throw in a little wind, it can get a little scary. I also pulled a 6X12 cargo trailer with the Trailblazer, the 6cyl engine had plenty of power, but if it was windy I kept a tight grip on the steering wheel. As was mentioned, you also want to think about cargo capacity, we always had a struggle with firewood, we usually just bought some after we got to our campsite as we didn't have enough room for it, plenty of room with a pickup.
We now have a Silverado with a 5.3L V-8 with the full towing package, including a bigger front sway bay and heavier rear shocks. I pulled the cargo trailer in 25mph winds a while back, could not even feel that trailer back there. The difference isn't just the engine, its also the suspension and the transmission. As to MPG, the Silverado actually does slightly better than the Trailblazer(then again Trailblazer's get horrible gas mileage for their size), believe it or not.
We actually pulled the X17Z back from the dealer, which is about 120miles away, in a 25-35mph wind coming at us from the front and side and I could feel the wind hitting the trailer, but the pickup never "felt" like it was something it couldn't handle. Of course we also have a WDH and a sway bar with the 17Z. I would not have wanted to do this with the Trailblazer.
It really comes down to how far and how often will you be towing. Plus, if you have a bigger TV, you could always get a bigger trailer:hihi:
2013 Starcraft Travel Star 229TB
2011 Jayco X17Z(traded in)
2010 Jayco Jay Series 1207(traded for the 17Z)
2011 Chevrolet Silverado 2500HD Z71 CC 6.0L/3.73
Reese "Pro Series" 800lb Trunnion WDH w/sway control