Not even knowing the model of the i3, Its definitely better. The on board graphics however be be better on the a4. But in Processing power the i3 will have it by far.
*EDIT*
Here is a Link to a CPU Hierarchy chart. The a4 would probably be on the block below the a6.
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.
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.
Not in the same ball park. The I3 is much more expensive and a much better CPU. Cheapest I3 is $115.00. AMD's cost alternative is a8-5600k ($5 cheaper on newegg).