Looks like row number may be more impactful on resources than using a counter variable in c# I assume?
Depends on the guts of the server vs the client(s) so it's pretty much impossible to say. Neither is free but the Row_Number function is pretty light weight (as TG says, it basically resolves as a sort) and will be resolved on the DB server which is likely to have plenty of clout. Putting your logic in the client effectively distributes the processing, which is good, but does so to machines that are likely to be less gutsy than a server. Really you have to try out both and see what you get.

If it's purely for display purposes across a small number of rows I'm kinda inclined to say keep it in the UI layer of the client but that's driven more by separation of concerns than performance.