Download this sample file
Unzip the two mp3 files, noting their current maximum amplitudes as indicated in the filenames
Open MP3Gain
Go to "Options -> Advanced..." and make sure the "Enable Maximizing features" option is checked
Set the "Target Normal Volume" to 92.0 dB
Click "Add Files," and add the two unzipped mp3 files
Do Track Analysis on the two files. Note that their volumes are only 0.1 dB apart
Without closing MP3Gain, listen to the mp3 files using your favorite mp3 player. Note how they're approximately the same listening volume
Now in MP3Gain, do "Modify Gain -> Apply Max Noclip Gain" (or press Ctrl-X). The two files are now peak normalized.
Listen to the mp3 files again. Even though their maximum amplitudes are now almost exactly the same, song clip 2 now sounds much too loud.