Sergey Rumyantsev studied migration from Georgia to Azerbaijan. He interviewed 460 ethnic Azerbaijani respondents who had migrated from Georgia to Azerbaijan. The majority of respondents said that the socioeconomic situation in Georgia was the prime reason for the migration. Ethnic discrimination did not play a significant role in the perception of Azerbaijani migrants (indicating that media reports of tensions between ethnic Georgians and Azerbaijanis may be overblown). About 80% of respondents still had relatives in Georgia. More than 60% of the migrants left for Azerbaijan in the early 1990s, when times in Georgia were particularly tough.
Rumyantsev also interviewed 170 Ingiloys (ethnic Georgians originally from the Qakh region of Azerbaijan), who had not yet migrated anywhere. Among the Ingiloys who were considering migration, only very few wanted to go to Georgia. Western Europe was more popular, followed by Russia. (The data obviously is not fully representative, which is why actual numbers might be misleading.)
Again, research (in Azerbaijani) with more findings available on our website, and even more information available if you contact the fellow directly.