The potential problem with the new program is that many programs share files. The program described (or at least most like them that I've seen) will show a file that updates a shared file on the computer as being "installed by the program." If you just delete everything that that installation did you may find other programs that quit working.
Many programs also detect files that they can share, and if the existing one is "newer" than what the installation has, it usually will not be shown in a log of changes made during that installation. If you rely only on log programs to remove stuff, the removal won't include shared files if the "other program" that used one has already been removed, or is using an updated version.
Control Panel | Add or Remove Programs is the only method that should be used to manage programs that appear there.
For programs that don't show up there, you should look in the program folder for an "uninstall" provided with the program before trying anything else.
Any "Windows compliant" program you install already makes a log file of the installation, so having a separate program to replicate information your machine already knows seems like a kind of redundant thing to do; but if you find it interesting to look at a separate copy you probably won't hurt yourself with it - as long as you've got the original installation disks for everything you might need to reinstall after you use your log file to uninstall something.