Pokémon: Let's Go, Eevee and Pokémon: Let's Go, Pikachu introduce support trainers, a second player who aids the first player in battling other trainers and in capturing Pokémon. When the two trainers throw Poké Balls and hit a Pokémon at the same time, the Poké Balls combine and there is a greater chance the Pokémon will be caught.
In Pokémon Adventures: Gold and Silver, Kurt explained that Poké Balls work by using a "capture net", which is very similar to a real net. In fact, in the manga, the gym leader Bugsy does use a real net with his Poké Balls. So in the hypothetical case where two Poké Balls hit one Pokémon, the result would be similar to two nets being used. The nets would interfere with each other and neither one would fully encapsulate Taurus. Taurus possibly would be immobilized for a short time before it broke free from both nets. In the anime it would glow red and become energy for a moment.
In the manga, Bugsy refers to his "capture net" as being the net that is supposedly inside a Poké Ball, but visible and already deployed. According to Kurt, this invisible net captures and physically stores a Pokémon.
As for better Poké Balls, such as a Great Ball, I would suspect their nets would be bigger and stronger, so they would be able to envelop the other Poké Ball's net and cancel it out. Thus, Taurus would be captured by the Great Ball.