"Many more" would normally be used with items which are countable. For example, "There were many more bananas on the upper shelf than on the lower one". If you wanted to, you could count exactly how many bananas were on each shelf.
"Much more" would normally be used with something that is not countable. For example, "There was much more sand on the left hand side of the river bank than on the right hand side". You can't count exactly how much more; you can just tell from the approximate volume of it.