Mine sound similar to yours but not nearly as big of a city. Valor used to run the show in the south end of our city and they owned every gym for the first few months. Even back with the old 1 'mon prestiging they owned everything.
Then Instinct started to slowly take over and pushed Red back a lot. It wasn't until the last month or so that Mystic (my team) finally started to make a push. Seems a lot of the newer players picked Mystic and we are now able to hold 5-10 gyms for at least a day or two before they get knocked down.
It seems Instinct is probably the most active with Mystic second. Yellow and Blue have split the south end in half and each have about 7-10 gyms each and for the most part we let each other have the gyms for a few days.
Red has been forced to move a bit further north and they seem to be content there for now.