If I use quarter sawn boards for the breadboard ends, the battens are stable but weaker.
If I use plain sawn boards, the battens are stronger but are themselves at risk of cupping.

Would one always be recommended over the other?
If I use quarter sawn boards for the breadboard ends, the battens are stable but weaker.
If I use plain sawn boards, the battens are stronger but are themselves at risk of cupping.

Would one always be recommended over the other?
I'd say go with quarter-sawn ideally.
Quarter-sawn wood can be relied upon to be much more stable, but it must be said many a breadboard end has been made from plain-sawn wood that has held up well over time.
Apart from stability there is the potential advantage in the figure on the face of the board, depending on the species you're using naturally.
If I use quarter sawn boards for the breadboard ends, the battens are stable but weaker.
I think you need to examine this, weakER doesn't mean actually weak. Any decently thick quarter-sawn piece is going to be innately strong in most woods, particularly in hardwoods.
To give some illustration that this isn't just a theoretical exercise the potential weakness doesn't seem to have been of concern to the makers of these pieces: