Down to trust really. I did an outdoor gig and brought my PA, I turned up and one of the other bands that was on later had their PA and it was seriously a professional many thousand of pound worth of audio equipment and a guy who clearly knew what he was doing, sound was fantastic. The next year they said that they were supplying a PA so I didn't bring mine, thought it would be great. It wasn't the same guy, it was 2 guys with with an 8 channel behringer analogue cheap mixer, a pair or standard behringer PA speakers and sub that was no where near as good as my PA, sound wasn't good.
Third year they said they had a PA too, so I brought mine anyway. As it turned out they had somewhere between the two and it was ok, but I don't trust it anymore, and if I have the space I will take mine.
Obviously you can wire yours up and chain the output to their speakers and see which sounds right.
I doubt it, if they have two inputs I assume they have two sides, so if you only plug into one you would only have one side of the system working.