FWIW, I remember listening to a grape radio pod-cast with one of the members of the Riedel family at Hospice du Rhone a few years ago. His opinion on this was, assuming you don’t have syrah glasses of course, do definitely use Burg glasses in preference to the Bdx. I can’t recall exactly what the crux of his reasoning was, but he seemed pretty adamant about it.
Pour some of the same wine in each glass and decide which one you like better. My wife and I do this occasionally with different brands/styles of glasses. Sometimes the results are not what you would expect. Given your OP, I would agree with some of the posters above, Bdx unless it is a Northern Rhone in which case I would likely use the Burg glass.
FWIW: The Riedel Vinum Syrah glasses are outstanding.
I know Zalto is doing a BerserkerDay deal…I just don’t have the details yet. It’s far too hectic a time to deal with wineries or retailers or distributors right now. January, baby…