There are far too many variables to give any straight answer.
Basically I would go first come first served however you have only filed FL340 and there are occasions where I would consider that and not climb you above FL340. If you want higher, file it. As we now have lots of flow control and vertical sector splits then you could be flowed in a lower sector and, by climbing to FL360, climb above the lower sector and fly through a higher one for which you have no slot. Its easy for us to work out what happens to that effect on short flights but as soon as you cross into another FIR then it all starts becoming unknown hence nothing climbing above filed levels. Other traffic can also become a factor be it slower in front or faster behind, and if your routes diverge or not in the near future. As I said, far too many varibles.....