Q+AL has been more successful than Q+PR because;
1) Adam is younger with a younger fanbase who in turn promote the shit out of it on social media plus mainstream media likely find a good looking and talented singer to be an easy sell
2) Adam has, in America at least, has had a far more successful career here as opposed to Rodgers whose solo success pales in comparison add to which Rodgers has nowhere the same name recognition on his own as opposed to the bands he was in
3) Q+AL also have performed on US TV and capitalized on that coverage whereas Q+PR as best as I can recall, never did. The closest Q+PR came to that was Queen week on American Idol and even then Rodgers was barely mentioned.
There are more reasons but i think you get the gist