Jeffmidtown -- I'll take offense to that "UVa rules the ACC" comment!

In response to your question, the eye size does not generally determine how strong a storm is...or, to better put it, while many powerful storms may have small eyes and many weaker storms may have larger eyes, the correlation is not very strong.

Many very strong storms can have very large eyes. Isabel and Frances are two such examples. Storms with larger eyes tend to be more stable intensity-wise, while storms with smaller eyes tend to be more unstable intensity-wise as a function of eyewall replacement cycles (the eye is less stable, meaning cycles are more likely).

There may also be some correlation between when a storm goes through many eye cycles, resulting in a large eye, that it is at its peak intensity and will not get stronger, but I'm not sure how strong that is (if at all); it is more my observations than anything else. Large eyes also tend to happen with larger overall storms, but again that is more my observation than anything else.