The grain does make a difference.
Highest grade shafts have grain running end to end with no run out off the shaft. As the shaft grade goes lower there is more and more run out. Too much run out and the dowel is only good for tomato stakes. Different companies seem to have different standards for what makes a premium shaft. One large shaft manufacturer says a certain amount of grain run out is acceptable on a premium shaft. I propose that they are making up their own standard.
If you're sorting through dowels at Home Depot or Lowes (Lowes has poplar) I'd go for the best grain possible. Crooked shafts can be straightened, but grain can't be fixed.
Guy