The differences in meaning are very slight. Disclaimer: I´m not a turk, only someone who´s learning turkish, so take my advice with a few grains of salt.

It seems like veya is used when you only have a few options.

- Çey veya kahve içmek ister misiniz? - Do you want to drink tea or coffee? - There are no other options is the subtext here.

Whereas ya da is more open ended

- Çay mý ya da kahve mi ister misiniz? - Do you want tea or coffee? - You can ask for anything along the lines of tea or coffee but those are all worth mentioning, all that come to mind.