As a bassist/guitarist I hear things that casual listens don't. So I have noticed that Timothy is more technical and rough then Randy. For example take a look at the Roc and Roll and Roll Hall of Fame. Hotel Califorina has a rough jumpy feel to it and in solo section he changed it up from Randy's original part.

Hall Of Fame.
https://www.youtube.com/watch?v=2dyw6LZpSOA
Capital Center 77.
https://www.youtube.com/watch?v=puHoadtIivc.

Now Randy has more of a smooth relaxed feel to a song and is subtle. Both of their vocals are amazing. Here is another comparison.

James Dean
https://www.youtube.com/watch?v=P5_0DzMVf1M
Heartache Tonight
https://www.youtube.com/watch?v=snPgFNMCXBs

Finally when the band brought on Timmothy also caused a change in the Rythym section with Randy was more of behind the drum beat and Timmothy was more on top. The changed made the Eagloes loose they're country sound completely and made it more R and B and Rock N Roll.