Pete’s answer is great.
Backbone models are inherently mutative, which (while not a problem in itself) means that when rerendering, you won’t have the old version of the model to compare to. This makes it harder to do intelligent optimizations by defining shouldComponentUpdate methods in key places on your components. (You also lose out on the ability to easily store old versions of your model for other reasons, like implementing undo.)
Calling forceUpdate merely skips shouldComponentUpdate and forces the component to rerender. Note that calling render is usually cheap, and React will still only touch the DOM if the output of render has changed, so performance problems here aren’t common. However, if you have the choice to use immutable data (including passing around raw model property objects from toJSON() as Pete suggests), I’d highly recommend it.