By far, the easiest for me to memorize are the songs that tell a story that develops verse by verse.

Songs where verses are interchangeable, that can be stuck in anywhere are much more difficult. In 'Give Me the Roses', for instance, there are two verses that basically say the same thing. To this day I often almost forget one or the other of them.

I use rhyme as an editing tool, not necessarily while I'm learning the song. In other words, if a couple of lines try to intrude into the wrong verse but don't rhyme...