Well obviously three cores is better than two or one - but you already have a healthy quad core cpu segment. Why would I want to get tri-core as opposed to quad? More cores is always better.
If you already have quad core then you would not bother getting tri core. It's just tri-core is less expensive then quad and about the same price as a decent intel dual core and better in some cases.
Quad core is brilliant when it comes to multi-threading applications or converting videos or music or whatever and it's future proof.But when it comes to gaming quad isn't really worth the money.You will better off with a tri-core or dual and a bigger gfx card.
http://www.anandtech.com/mb/showdoc.aspx?i=3533&p=9
When it came to actual game play experiences, our opinions still have not changed when it comes to a choice between the Phenom II or Core 2 Quad. The Phenom II processors are a better choice in Company of Heroes: Opposing Fronts and Crysis Warhead due to fluidity of game play, especially with background tasks running or CPU utilization near 100%. In the four other titles, we could not tell any real differences in the quality of game play between the Phenom II X4 940, Phenom II X3 720BE, or Core 2 Quad Q9550.