I reckon the Torx design is basically sound. It's superb with aerospace fasteners.
The problems arise when manufacturers use a relatively large screw, with a relatively small Torx recess, generally on those 'button head' screws like the one shown.
These things crop up everywhere and are always a pain. In a way, you're lucky the bit broke. Usually now, the screw is made of cheap monkey metal and the recess gets churned up!
Decent bits, in my experience, are Snap On, Stahlwille, Hazet, and KoKen, but there are others!
Attack the thing with a decent bit first! If the screw recess starts to go, then use the cheapest bit you can find and a blob of weld! Then replace the screw with something decent! Where I find these a lot (brake discs / rotors) I keep boxes of decent replacement screws on hand!
Beta tools offer an almost unique 10 mm hex bit system with a 1/2 inch drive bit holder and 10 mm hex bits. The advantage of this is you can get the bits in the larger sizes for brake discs such as T55, but the bits are very reasonably priced so you can afford to weld one in if you need to!
If you're on a budget, this is cheaper option than the usual Torx bits, each with their own holder! The bits seem decent too!