There is no way to guarantee that the make uninstall process for the new version will do the right thing with the version you have installed. You'd also need to make sure that you had identical configure options with your new and old version. The risk that it will do the wrong thing is just too great, especially if you're running this as root.
This is one of the many reasons why building proper packages for your system is so useful. Creating Debian or RPM packages is not hard, and there are tools like dh-make, which give you 90% of the work required, especially for autotools based packages. The advantages of using packaging are that when you upgrade, you know that none of the files from the previous version are installed and that you know what files the package has created on your system. You also get to keep the knowledge of how the previous package was built and can repeat the build with newer version. If you compile from source using "./configure; make; make install", there the chance that you'll lose knowledge of what options were used, what process you used, what patches you applied.
These advantages are definitely worth the small investment of learning to package your own software.