Is it a good idea to move the battery?
 

I have a 1302 and was wondering the pros and cons of moving the battery to the front?

On the paper it is not a bad idea. The weight balance front/rear will be slightly better. You had to take care about the right cables lenght & diameter (25-30mm2) to extand the location to the front and a battery box if you battery is using liquid acid. (News batteries with gel do not imply a battery box).

I've seen riders that keep the battery on the opposite side of the driver side but I'm not sure it changes many thinks

The current battery position is at the neutral axis for the chassis so it has little effect on the handling. Move it to the front and you are adding around 10kgs (depends on the battery) to the wheel load, which is a small amount. On the minus side:
1) The roll couple is increased (not necessarily a bad thing though)
2) The polar moment of inertia is significantly increased - 10kgx2m(ish) = 20kgm (about a 1/3 of PoM of the engine) This will dull the chassis response as the interia to overcome the resistance to turn is increased.
3) There will be a weight penatly for the cable for the starter that will need to be quite hefty so as not to drop too much voltage.

Clive

On the positive side you will move the axis of rotation forwards and have better weight balance for steering...