"Friendship" is such a 19th century way of putting it. 
Haha.

I'm trying to think of a piece where both Thalberg and Liszt did paraphrases. You no doubt know their efforts in this territory better than me, but I have the initial impression they didn't much tread on one another's toes (or perhaps didn't enter crowded markets)?
Offhand, Robert le Diable, Rigoletto, Il Trovatore, Norma. La Sonnambula, Lucia di Lammermoor and Don Juan (plus both contributing to Hexameron) but yes, when you consider they wrote over 100 between them, there isn't as much overlap as might be expected. Of course, while history has them down as competitors, there were plenty other people around at the same time, also churning out paraphrases: Fumagalli, Prudent, Pixis, Herz, Moscheles et al.