You can solo queue both, but not do it while in a group. You can only choose one or the other with your group. We used to have a work-around where we'd group queue WZs and both solo queue GSF at the same time, but they removed that ability when they allowed Republic and Imperials to play on the same team in GSF.

GSF would pop more often if the Devs would allow us to group queue for both WZs and GSF while running together with friends. I know my friend and I love all PvP, but we hate having to choose between GSF (our favored one that rarely pops) and WZ queues. Devs, Please allow dual group queuing!!!

Though GSF pops far less than WZs, my guildies and I used to solo queue GSF and group queue WZs since almost every GSF that popped would allow us all to go in for the same match. It was a poor man's way to group queue for WZs and GSF matches. After the last major update, this is no longer possible since a group queue for either one disallows solo queuing for the other, and so we almost never queue for GSF anymore (where before we were always queued). Devs need to allow for group queuing for GSF *AND* WZs at the same time to help with pop rates for GSF. There are those of us who want to do all manner of PvP with our friends and guildies, but we're now stuck to waiting forever for GSF or playing WZs and giving up on GSF. Devs, please address this minor change which will make a major quality of life improvement for those of us who still love GSF and lament having to choose between playing now and waiting forever. At the very least, allow us to solo queue GSF if we are group queued for WZs, so we can still play with friends on whatever pops first.