protected vs public constructor for abstract class? Is there a difference?

They are the same for all practical purposes.

But since you asked for differences, one difference I can think of is if you are searching for the class’s constructor using reflection, then the BindingFlags that match will be different.

BindingFlags flags = BindingFlags.Public | BindingFlags.Instance;
var constructor = typeof(MyClass).GetConstructor(flags, null, new Type[0], null);

This will find the constructor in one case, but not the other.