Greaseproof paper’s strong point is that it doesn’t allow water or oil to permeate through it. However, the cake mixture will stick more securely to greaseproof paper. So while greaseproof paper is moisture & grease resistant it can be harder to peel off the baked product. It’s advisable to make sure the mixture completely covers the liner, as the wax coating can melt under high temperatures and while it is unlikely, at very high temperatures it can catch on fire. (We personally haven’t ever experienced that though).
Baking paper is better if mixture is something that is likely to stick (e.g. meringue and high sugar content recipes). Baking paper is treated with a food safe acid during the production process which makes it very heat resistant and will continue to be non-stick after exposure to higher temperatures.
Because baking paper can withstand higher temperatures it is ideal for desserts and pastries which cook at higher temperature than muffins and cakes.
Bear in mind though that baking paper may come away from the sides of cupcakes or muffins after baking.
It is the same type of paper that is often used to line cake tins and biscuit trays, so mixture doesn't stick!