Like already said I use Skyns latex free as I have a reaction to latex condoms, the thinner Elite ones are my preference as I get a better feel as well as the client. Mine come from online too as much cheaper to buy that way in bulk.
I also carry them in large and king-size and have passant trim for the smaller gents and to go on my strap on, all are latex free and don't taste unpleasant if doing OW.
Durex I find unreliable and they have a terrible taste if doing OW I'm not sure if it's the spermicide they use of if there is some kind of delay effect to them but they make my mouth go numb, that may be one particular type of durex though, I've not touched one for years thankfully.
I'm not adverse to a client bringing his own but it would have to be in a sealed packet and latex free so only any good if discussed beforehand and those conditions were met.
For me the most important thing is getting the right size for the job in hand and ensuring its fitted correctly.