I no longer prototype but go straight to a PCB. But I used breadboards for years (decades really) to good affect and they are easier than soldering onto strip board so I would say use breadboards for an initial pass at a design or if you just want to quickly experiment with a new chip etc.
Just be aware of their limitations, mostly WRT potentially unreliable connections.
Use strip boards if there's any chance the design will become permanent or if you want to use it somewhere off the workbench.
Rob