It is not clear that Rava decided not to pay Bar Hedya. Rather, no payment was requested (just as one does not pay a Rav for answering a She'eilah). Perhaps payment was voluntary, and Abaye had the means to pay Bar Hedya whereas Rava did not. It is also likely that what irked Bar Hedya was not so much that Rava did not pay him, but the contrast between the two: that Abaye did pay him and Rava did not.

Another possibility is that Abaye paid voluntarily because he was an outstanding Ba'al Chesed (as the Gemara mentions in Rosh Hashanah), who would give away money even when he was not obligated to do so.

B'Virchas Kol Tuv,

Rabbi Chrysler