I'm guessing you mean biggest, not buggiest. Buggiest would definitely by July 4th on the Esplanade.
Biggest? That's really hard to say. Generally, I'd say that Head of the Charles was the smallest. It was a lot of fun to work, but that's beside the point.
First Night depended on the weather. Generally not a lot for the police to do and EMS mostly deals with drunks. Except for the year that some nitwit in a SUV got impatient and ran over half a dozen pedestrians down near Long Wharf.
The last "Wolling Walley" I worked was for the Bruins Stanley Cup. It was also the largest and the most rowdy.
Except for 2013, the Marathon is a long day, but EMS calls usually peaked from 2:00PM to 4:00PM. Before and after, it wasn't too bad. Unless, it's very hot and then we'd get runners and spectators dropping.
July 4th was probably our longest day. They hotter it was, the busier we got. Lots and lots of minor stuff, and occasionally a serious medical or trauma case.
As far as monitoring, the frequency/TG list is pretty stable at this point. Despite having a mix of conventional, trunked, UHF, some VHF, and various agencies, the Interop is very good. Lots of patching and a good deal of interagency cooperation that you don't hear because it's not over the radio.