Per this question, there is an extra item involved when spinning your own team's gym disc. Is it better to spin as much of these discs because of the possibility of getting better drops from these spins as opposed to discs at gyms that other teams control (e.g. better balls, higher potions, better change for upgrade items)? Or is the drop rate the same regardless of who is in control of the gym?
Short answer: No.
Now that this system has been live for a few months, it seems safe to say that based on the lack of evidence otherwise, the drop rate for the bonus items awarded when spinning a same-team gym photo disc is not more weighted towards rarer items than the other items awarded by spinning a photo disc at a non-same-team-controlled gym. That said, while the individual likelihood for any one awarded item to be a rarer one is the same, you do receive extra items, which in turn makes it easier to get one of those rarer items.
It may be worth noting that different drop rates for spinning a gym photo disc versus a Pokéstop seems to be possible, based on data such from threads like this one, which reports roughly a 5% better chance to get a potion, revive, or berry compared to an earlier aggregation of drop rates for Pokéstops, but based on the findings there as well as the comments alongside it, rarer items (like the coveted evolution items) don't seem to be more likely.