This part depends how bt programs are tweaked, so your fittter should be able to help you with that.
Plus for bt media streaming, you have volume buttons on aid itself or you can use phone app, with both you can adjust how much environmental sounds should pass through.
Same is with tv connector, it has own program which can be adjusted as needed.
Main difference is in having program for each, so in case you use them in distinctively different situations, ability to tweak them with your fitter can be valuable.
Second one is that battery drain on HAs is roughly three times lower if you’re using tv connector as opposed to bt. For rechargeable battery, and zinc airs show similar behaviour, but can’t confirm the numbers exactly.