There are pros and cons to treadmill versus on-street gait analysis.
Running on the street is probably more natural and unrestricted, where as a treadmill can have a small effect on your gait.... but the on-street observer can't slow a video down and show YOU how you're running, which I find interesting. The skill of the observer is important... and probably moreso for the on-street option, because by its nature, you soon disappear from easy viewing distance - someone watching you on a treadmill can take their time and do this comfortably, and also use the video for analysis too.
I've had both - and both came to the same conclusion about my gait, which is encouraging. In conclusion, I'd say that if I could guarantee to have the very top biomechanic expert to analyse my gait, I'd choose the street. But on balance, I'd suggest that someone with a decent reputation with a treadmill would normally be the better option. I preferred the treadmill experience. But I wouldn't knock either method.