Apologies, was out of the house all day.
3-pin fan speeds are usually controlled by voltage levels, while 4 pin fans are usually regulated via duty cycle, hence the PWM or (Pulse Width Modulation).
I'm going to go with, the fans should work together but are not compatible. The 3-pin fan should function at full speed in a PWM situation, since it has no method of working with any PWM signal being fed to it. Probably best to get matching PWM fans, if that's the method the fan controller is going to use. Some motherboards let you choose between PWM or Voltage control, but this is very hit or miss and also you find mixes of fan controllers on the same motherboard, where some are not controlled at all, some are PWM only, and maybe one or two are PWM or Voltage control, but never both types of control at the same time, as that isn't possible. Of course, voltage control isn't likely to work for your PWM fans, so you're going to have to decide which you want to go with. Might as well pick PWM, as that's the current standard, and just upgrade all of your fans you want to be controlled to that. You wouldn't need to upgrade any fans you don't mind running at full speed.
And of course, there is always the caveat that, if you go totally overboard and buy crazy powerful fans that blow hundreds of CFM of air, you may over stress the fan controller. There are limits, and having more than one fan on the same controller just adds to it. You can see the power draw of your fans on the back, usually on the backside of the hub where the motor mounts.