I think Beerus held back severely against Goku the first time around. It's clear that he's still on an entirely different level from Goku, likely even with Kaioken, although that might not make sense to some. Even if Goku could hang with Beerus with Kaioken x10, how long could he even maintain the power? Not very long at all I assume compared to what Beerus could keep doing.
Also, I suspect those last few notches of Beerus' power that he didn't unload on Goku would likely equate to an almost 50-100x multiplier in comparison even to Goku's Blue Kaioken x10.
Even if not so powerful, Beerus very likely wins out based on the fact his body is more capable of handling the power over long stretches compared to Goku's.