There is some network design issues that worry me about your description, but, to answer your question..
You can run 10mbs, 100mbs, or 1000mbs on a piece of Cat5 between the closets. You can run 10 mbs, 100mbs, 1000mbs or more on a fiber between the closets. The media has limits on top speed and performance, but, the actual link throughput is based on the hardware on each end as well.
If it were my installation, I think I would run the fiber and be prepared for a higher speed backbone. However, just because you put fiber in doesn't mean it will increase the speed of your network. Seperating the three hubs into different switched segments would definately be worth the trouble.
Daron J. Wilson
Telecom Manager
LH Morris Electric, Inc.
daron.wilson@lhmorris.com