harmonies were definitely more complex than many songs. Their gift of writing catchy melodies and then pairing their voices together in a way that drew in the listener easily was pure genius and has rarely been approached since. Maybe the Eagles were another band that could do that. The common thread is two co-writers that both were great writers apart but as a combo were better than the sum of their parts, AND they could both sing harmonies AND their voices had a great blended sound.

I don't think any of this reply will help you sing their songs better. Changing the key the song is played in (I assume you are accompanying yourself on guitar or piano, not doing Karaoke) might help in some cases.

My son (14) is way into the beatles and started playing guitar several months ago. All he wants to learn is beatles songs. He could sing them great in his "boy" voice but now his voice is changing and he is having a tough time singing some of them so it makes sense.