The mic in the camera is not bad but it lives in an unfavorable acoustic environment. Being back where a camera is optimally positioned for image capture, puts the audio capture in a terrible position for optimum quality. You are going to have to think of two different systems and optimize each. Getting the cheapest mic out there, close and in a primary direct sound field with limited reflected sound or in reverberant fields will reveal that the built-in mic is better than you think. Both the external mic and built in mic are suffering from high ratios of indirect sound to direct sound. If it is a fixed performance where the sources are set, mount a mic or one of the several miniature digital recorders in close proximity to the source and mix the field sound back into the video in post processing. You can also ask for a house mixer feed which would be the PA mix of the mics on stage. In each of these cases, reducing the ratio of reflected to direct sound will make a world of difference. A $1 electret mic element close in will sound better than a $5000 mic bathed in a sea of reflected and delayed sound. Another issue to consider is sync between sound and visuals. The image seen in playback is seen with the optical magnification of the longer lens so distance presents no delay in imagine(light is essentially instantaneous) But sound travels very slowly in air, about 1100 feet per second so even 30 or 40 feet away from the source will present enough delay between the image and sound to have human listeners disturbed by it. You can add delay, or slip the video but the best way is to capture the sound close to the source so it solves the problem of syncing sound to picture. So two big problems are solved by using remote mics near the source, without regard to the overall quality of any particular mic. Any mic in a great acoustic space will sound better than the best mics in a bad space(one filled with stronger reflected sound and reverberant field) just like any camera and lens in a great light situation will be better than terrible lighting with the best cameras. It is just as dramatic a difference with sound as with light.