When a research agreement has finished and you receive your free technology, does your research partner receive the same technology? I would guess that both parties receive one of their respective "next" technologies, which may or may not be the same, right?
Update: This question has been made obsolete by the June 2011 patch. Research agreements now give a tech boost instead of a free tech. Tech boosts start at 50% of the median value of all techs you can research. Can be boosted to 100% if you both start Rationalism and build the Porcelain Tower.