The bots are good for rapid factory expansion, but they come at a cost. Bots require more computational power than belts and this is the reason you won't be able to build the biggest factory possible. Your framerate will start to drop at some point and because of the factory expansion speed (without belts) you'll reach that point quickly.
The belts take much more time to build and manage than bots, but also less computational power. So in the long run factory with belts will be bigger and you'll be able to produce more goods per second with the same computational power.
To say the truth I never got to the point where belt based factory was so big, that my framerate started to drop. Im a bot person, but my games ended quicky thanks to that.
That's the core of Factorio, to produce as many items as possible.
Let me show you some graphs:
BELT BASED FACTORY:
![Image](https://s19.postimg.org/fddbhri83/2018-01-05_1.jpg)
BOTS BASED FACTORY:
![Image](https://s19.postimg.org/dlkcmwwb7/2018-01-05_2.jpg)