By yourself or with the family? Those are totally different vibes, two cities that could not be more different. And the fishing reflects that.
Cabo is Newport Beach South. Richly appointed hotels, crazy nightclubs filled with rich anglos from America and Europe. When they go fishing it is 90% yachts and upscale cruisers. Cabo is more vulnerable to Pacific hurricanes, and in September that is a possibility. La Paz is a city too, but centuries older and bigger and not nearly as fashionable. Anglos don't go to La Paz for bachelor or bachelorette parties, they fly to Cabo. But the fishing is great at that time of year in La Paz, and both cruisers and pangas are available.
Between those locations is the East Cape, and is by far my favorite location in Mexico. Not a city at all, shopping is NOT going to make your lady smile. But the fishing is close to the best in North America, and is especially fun from a panga. I would rather spend a week at Rancho Leonero than anywhere else, my first choice in all of Mexico.