Being the same weight or even lighter is not a large concern. My TV is almost identical in weight to the TT (see signature), right at 3 tons each. The trick is to have enough horsepower to get the job done, enough brakes to get it to stop and adequate weight distribution and tongue weight to keep it stable (aided by anti-sway devices or hitches).
Look at the HD pickups... Most of them are rated to tow way more weight than the weight of the pickup. RAM HD2500 with the Cumins Turbo diesel is rated to tow over 12,000 lbs., while the truck is less than half that. Weight of TV isn't directly bearing on the tow capacity or safety. More is better, but, not mandatory. The "build" of the TV is, however; you want horsepower, torque, frame rigidity and weight carrying capacity.
The longer wheel base on some vehicles aids greatly in towing control and maneuverability (a longer wheelbase will make backing the TT much easier). Any good sized SUV or smaller pickup can quite safely haul your TT if it has enough horsepower and a weight capacity to handle the passengers, cargo and tongue weight. Despite the most common chant "get a 3/4 or 1 ton pickup", they really aren't necessary unless you are planning on upgrading to a 5th wheel or a TT exceeding 28 or 30'...
Look around...you should be able to find a TV that fits your parking space and will still safely tow your trailer and it doesn't' have to be a pickup truck. My Commander will fit into any parking space not marked "compact cars only" and there are many other "non pickup truck" vehicles out there will do the job for you.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)