I don't know for certain, but it seems like const
strings would be allocated differently. In particular, they won't be eligible for garbage collection. So it's likely that they have less overhead associated with them than do strings loaded from resources. The difference, however, is likely to be very small. Unless you have a huge number of strings, you're not going to notice a difference in your heap memory usage.
const
is used for things that never change. Resource strings are for things that are likely to change. Your decision on which to use should be based on that, not on which one takes more space on the heap.