Unfortunately, for us as normal, everyday people there is no really good way to tell how dangerous a swarm is.
As Kate Gregory, has mentioned, usually a swarm is the most docile a bunch of bees as there ever was. But there is one fact that trumps all that: we people are stupid.
With normal bees and normal people it would take something like 1,100 bee stings to kill. Granted, it would suck long before that, but for normal bees a normal adult can withstand 10 stings per pound of person. Of course, if you're allergic it could take a lot less.
Even "killer bees" or "Africanized bees" still take that many stings. The "killer" bees are just far more likely to attack, and attack as a larger swarm then "normal" bees.
So, angering the swarm of bees is a bad idea, and you should just stay clear. You are far more likely to be hurt "acting a fool" around the bees than to be actually hurt by the bees.
The swarm itself is not very dangerous, but like many things in nature, not respecting the situation could get you into some real trouble. Your best bet is to remember what our mothers all told us, "If you don't mess with them, they won't mess with you" and move on. If you don't want the bees there then call a beekeeper or pest control depending on your own personal preference.
https://www.ars.usda.gov/pacific-west-area/tucson-az/honey-bee-research/docs/bee-stings-safety/ is a good read