Just a little math...
A BB with a T PA will hit a 19k ton BR on a 6 (72% of a hit), doing 1 critical and 4 rolls on each of the Surface and Radiation (Which boils down to about 3 weapon hits). With a 1/3 chance for a mission kill from the critical (Depending on the setup of the BR. I am assuming they have Frozen Watches and extra computers), that results in about 4.2 shots per mission kill.
The BR needs a 8 to hit the BB with it's J Meson, a 9 to penetrate the Screen, then a 6 to penetrate the Configuration for a total of 8.4% chance to do damage (And 70% to get a fuel tanks shattered result. Including the mission kill criticals, each shot that does damage has a 87.3% chance to mission kill the ship. If it doesn't mission kill the ship, it will send it to reserves to repair for a couple turns likely). Roughly 12 shots per damaging hit, 13.6 shots for a mission kill.
If the Battleship had a T Meson, it would need a 10 to hit, 5 and then 3 to pen..13.5% chance to get a kill. Roughly 7.5 shots per kill.
If one empire uses J meson 19k ton riders, and the other uses T-PA BB's, the one with the Battleships will likely have an advantage. It's a game of rock paper scissors. The BB's with the T-Mesons also stand a chance, but likely the BR force will outnumber them 2-1, rendering thier advantage less. The T-PA has a 3-1 kill ratio.
For what it's worth, every 20 Nuclear missiles against a BB will do some damage, and it takes 35 Missiles to do damage to the BR. (Assuming Factor-9)
Granted, all the math on the spinals is thrown out the window if you use bigger Riders with T or N guns. When I design a fleet, I make sure I use a mix of bigger riders, with some carrying the T PA as well.
One advantage the wasn't listed for BB's over BR's is the pilot limitation. Most systems limit the total number of pilots in a force, and the BB uses half as many pilots as a BR plus Jump Shuttle. Granted, this also encourages Multi-Rider Tenders.