Deidara learned that Naruto was searching for Itachi and Sasuke. So he and Tobi headed their way, stating it doesn't matter if they encounter first Naruto or Sasuke, because the Nine-Tails was their target and Deidara also held a personal grudge against Naruto himself due to their encounter from earlier.
For Sasuke, he wanted to take him down for killing Orochimaru as he himself desired to do so, for he betrayed Deidara's former partner, Sasori and the organization itself. Deidara also secretly hated Itachi for offending him and his art and forcibly recruiting him into Akatsuki, so killing his younger brother would also serve as a kind of revenge for that. They just happened to meet Sasuke first, that's it.