The Core i3 is has a much stronger processing core regardless if it is the 2nd generation Sandy Bridge or 3rd gen Ivy Bridge.
The A4-4300m has a weaker CPU core. The integrated graphic core Radeon HD 7420m is also pretty weak. Based on the game benchmarks in the below link the Radeon HD 7420m show that in general it is even weaker than the Intel HD 3000 graphic core found in the Sandy Bridge CPU.http://www.notebookcheck.net/AMD-Radeon-HD-7420G.77224.0.html
Regardless whether you get a laptop with a Sandy Bridge or Ivy Bridge CPU the Core i3 is totally more powerful than the A4-4300m. You want an Ivy Bridge Core i3 though since the Intel HD 4000 is generally about 35% more powerful on average than the Intel HD 3000.