Mostly it boils down to personal preference and stereotypes.
With one exception - depending on the brand, and your need for BT streaming (think 8h or more daily), since brands (phonak) might not hold the charge for whole day. Rough estimate is 10% battery less for each hour of classical BT streaming. Tv connector streaming eats significantly less, let’s say around 3% per hour.
And you probably want them to hold you whole 16h day.
If you don’t BT stream so much on phonak (eg stay under 4h of bt and 4h of tv as they estimated), you’re good.
Those who use btle will eat less battery (eg everyone else except phonak /unitron).
In other words - don’t forget to stress test the HA endurance for your heaviest imaginable (but still realistic for you) use case and you’ll get your definite answer.