Sometimes generic is allowed to use the same ingredients to make a name brand product. Always check the back for both of their ingredients. (I know for a fact the mouthwash Lysterine will not allow generic store brand to use their ingredients. Lysterine is the only mouthwash with its ingredients.)
Medicines supposedly are the "same" just different manufacturers. (I don't work in pharmacy so I am not sure if it is true) However I do know that certain medications (the ones that work with the chemistry of the brain) do not work as well or has different side effects for people just by having a different manufacturer. If you find one that works DO NOT change it!
But you asked about eye drops..... Sorry. LOL! I would talk to the pharmicist.