I've towed ~7k lbs quite often across the country. Typically my xcab on an 18' 12k trailer.
I've towed with 03 Dodge Cummins, 04 Tundra, 06 Tundra, 11 Tundra CM, 06 Tundra, 15 Tundra, 16 F350 PowerStroke.
There is no comparison between my F350 and any of the Tundras. Much easier to tow with - easier to accelerate, safer braking, less movement when being passed by tractor-trailers or in wind, less struggle to get up hills or deal with traffic.
With the Tundra's, towing was what I call "active" driving... it took more concentration, more planning (for merging, etc)… So just because my Gen1 Tundra's were rated to tow the load, it's hard to say it did it with as much ease or confidence.
EDIT: One complaint about the Gen2 Tundra - tow-haul mode in the transmission. I overheated my 11 crewmax's transmission driving through Illinois... and struggled with my 15 for similar reasons... the tow-hall doesn't lock out 6th gear. Damn thing would hunt. So I ended up manually shifting and staying in 5th. Buddy has an 09 - has the same complaint. Fixing that would have made the towing experience easier in the CrewMax. I always towed in Drive on the gen1's... the 4.7 was happy @ 3k RPM's.