A 13 over bike has a gear ratio of 13/18, which means that there are 13 teeth on the front chainring and 18 teeth on the rear cog. This is a relatively low gear ratio, which makes it easier to pedal up hills. An 18 speed bike has a gear ratio of 18/18, which means that there are 18 teeth on both the front chainring and the rear cog. This is a higher gear ratio, which makes it more difficult to pedal up hills, but allows the bicycle to travel faster on flat ground.
Ultimately, the best gear ratio for a bicycle depends on the type of riding that you will be doing. If you plan on doing a lot of hill climbing, then you will want a lower gear ratio. If you plan on doing a lot of riding on flat ground, then you will want a higher gear ratio.