I’ve never listened to a Jambox or this unit, so I really can’t be certain.
But just by going off the spec sheets I would suspect this unit goes quite loud. They’re claiming that they have a 150 watt amp in the thing and they are advertising it on their Kickstarter as being suitable for karaoke and delivering presentations. Now, they don’t specify what the per-channel rating is on the thing. But Axiom tend to be straight shooters on specifications.
Googleing around a bit and it looks like the Big Jambox has an 18 watt-per-channel amp in it.