Wow - I wouldn't be comfortable with my 13 yr old in a large venue even if dad is watiing outside. You don't say who is performing - which would have a lot to do with who is in the audience. What kind of a crown do you anticipate? How would they handle a situation if someone tried to take advantage of them for their money, their cell phones, etc.? Do you think the two of them can navigate the facility on their own? Do you think they can handle a situation where they get separated or one gets sick? Are they both the same gender so they can acompany each other to the rest room?
I trust my children but not so much the people around them. I've taken my 14 yr old into the city (NYC) and asked her to figure out which subway or bus to take to penn station, or who is a good person to ask for help (a lady who looks like a mom because women are far less likely to be predators, and police officers can not be expected to be nearby all the time). So while I think she could handle a tough situation if she needed to I wouldn't put her into it at this point voluntarily.
Sometimes I think we're in a rush for our kids to be little adults, or to have older teen experiences before they're ready for them. I usually tend to err on the side of caution and allow my children to be children until they're ready to be young adults. Usually the kids are relieved when they're told no. They may not express it to you, and will act like they're mad, but deep down inside they are looking for mom and day to control stuff.
Good luck mama - this is a tough decision. Ultimately, you know your kid, hopefullly you know this other kid, and the dad. Taking all that into account the the type of crowd that is anticipated you need to go with your gut. Soemtimes the decision is easy, sometimes it's not. This parenting stuff is not easy!