When working with packages it is better to use yum than rpm directly so that dependencies are observed and maintained.
As I read the OP he specifically wanted to install "not through yum". I guess he had his reasons which he did not state, so my reply was targeted to his question as he put it.
The advantages of yum as stated above in relation to taking care of dependencies is the case as I understand it.
In relation to the $PATH variable taking care to execute /usr/local/bin before /usr/bin, that would the be case if the executable directories are in that order in the $PATH variable, which is the default in f19. However, $PATH is configurable and the order can be changed. The OP was silent on that score, so I made no assumptions.
In relation to conflicts between the two versions of make, I take the point that it is possible to keep both versions and that they may not conflict if the $PATH variable is set at the default. However, I can't see the point of keeping a redundant program. The logic of doing that escapes me. But I suppose that my reference to conflicts comes from my experience with not deleting redundant programs in just such a case as the OP describes, where one is in the packaged system and the other is in the /usr/local system. The conflicts I had did not occur with the executables in /usr/bin and /usr/local/bin but with the libraries associated with those executables based on the differences between /usr/lib and /usr/local/lib. These were subtle problems that I had trouble working through at the time, hence my reference to conflicts and my suggestion to remove the redundant program.
As suggested above, the new make may need updated versions of its dependencies installed, so that would need to be attended to.
A further point about yum and rpm is this: if one is not on broadband, yum is not a viable option for many users of a large distribution like fedora because to keep up to date with yum involves downloading hundreds of megabytes of data at times to update programs and dependencies and this is not realistic on dial-up or other slow internet connections. For example downloading at 5 minutes a megabyte on a dial-up connection would mean about a 16 hour download for 200 megabytes, and most dial-up providers in these parts allow 4, 5 or 6 hour windows to the internet, so it's very problematical and very painful. My point is that the conventional advice of "use yum" may not actually hit the mark for all cases. In fact there are ways of dealing with "dependency hell" using rpm, but that's a different topic.