I find it a little strange that Apple did not increase the RAM on the iPhone 5S. A 64-bit compiled binary is typically larger than its 32-bit counterpart and consumes slightly more RAM, too. If Apple recompiled their iOS libraries, applications and services for 64-bit, I would suspect there is less available RAM on the iPhone 5S than 5C or the original 5.
Only when comparing 32-bit iOS 7 to 64-bit iOS 7 would that be relevant without knowing how iOS 7 deals with RAM compared to iOS 6. We'd also have to consider how much the device has to spare compared to how much extra is needed over 32-bit. Based on performance, including iOS 7 on older iPhones is say they dealt with that issue very well.