We can very easily math out which stat is better, assuming the proposed values on the JP wiki are correct (particularly for Rush's increased double attack rate).
If Stinger gives you a % chance of doing +20% damage (otherwise known as critical damage), then the value of Stinger is %_Crit/5 (compare to Assault, which is usually +character_attack/2). For SLVL20 small, that's +2% overall damage.
If Rush increases double attack rate, then the value of Rush is approximately +%_dbl*(1-%skill_damage), as Rush contributes to normal attack damage and Burst damage (via more frequent Bursts), but not skill damage. I'd roughly weight this as +%_dbl/2 or +%_dbl/3, since you're typically going to be holding your Burst in tough battles. For SLVL20 small, that's +0.5% overall damage. Again, this assumes that Rush increases double attack rate as little as the JP wiki says it does.
In short, use Stinger if you'll have elemental advantage. Otherwise, use Rush. Assault will always be far better than either of these.