When it comes to coils, this is a tough one to answer. Certainly for different types of detecting, having a smaller or larger coil can be an advantage. But 90% of the time the stock coil will give you good results for coinshooting.
There are two main types of coils available, concentric and double-d (DD). Knowing which type your detector uses helps you understand how to get the most out of it. A concentric coil puts out a cone-shaped field (shaped like a O), the DD field is more like the "center slice" of the concentric (shaped like an I).