depending on the model, typically a i3 has higher level 3 'cache' (3MB vs 2MB for the Pentium) and the i3 also has HyperThreading which makes it 'appear' that its a Quad Core, even though 2 of them are only logical. It makes what the i3 is doing with its 2 REAL cores more efficient.
Hyper-threading doesn't have a strong effect in something like gaming, although some people might debate me on that, but in tasks like video edit, people can see a 10-20% increase in performance depending on system configuration.
Check this link http://ark.intel.com/compare/53492,53422 it should give you a quick way to see the difference between these processors. In the end it really comes down to 2 things; clock speed (Intel® Core™ i3s are faster) and Hyper-threading (the Intel Core i3 has it). The value of hyper-threading on a dual core processor is higher because it does come into play more since more applications (including games) can use the additional threads. Once you reach to about 4 threads very few applications can take advantage of more threads past that point. So Intel Core i3 will use the hyper-threading a lot more then an Intel Core i7 will.
Christian, thanks for the info! But to jump from a P to a i3 to get Hyperthreading is sometimes a 20-30% jump in price, and I guess my main point is while you get a jump in performance for games, its not near a 30% increase in say, frame rates. So, if a gaming build has a limited budget a P will do great, where as if there are more CPU heavy tasks like video, something with HT would be more justifiable to commit more budget to it...