If you branch or copy the project you're creating a maintenance nightmare for yourself down the road.
Create a separate target in the same project, specific differences can be handled via #ifdef blocks in the code. Add defines to each target to specify whether you're building paid or free versions.
== ADDED ==
To define the per target symbols go to build setting for the target, scroll way down until you find the Apple LLVM 5.1 - Preprocessing block, the change the target-specific settings to add your desired symbol (FREE_BUILD=1 or PAID_BUILD=1 e.g.)
To add target specific code you can then use that defined symbol in your code as:
// some code here
#if FREE_BUILD
// Some code that only gets compiled for the free target here
#elif PAID_BUILD
// Some code that only gets compiled for the paid target here
#else
// Just in case because I'm a paranoid sob
#error Must define FREE_BUILD or PAID_BUILD
#endif