Very difficult...
I'd probably say Broken Sword as I've loved that series way longer than Gabriel Knight, but... I dunno. If I played Broken Sword: The Shadow of the Templars, Gabriel Knight: Sins of the Fathers and The Beast Within - A Gabriel Knight Mystery, it would most likely be in that exact order. I love those three games!
Although the Broken Sword series only has one game I love (no. 1), with 2 and 3 being very good/great, Gabriel Knight has two I love (no. 1 and 2) with just no. 3 that I think is very good/great. Both are fantastic series in their own ways - they're exactly the same but different.
I love Broken Sword for its more cartoony-upbeat/lighthearted nature, which certainly doesn't lack in murder mystery, intrigue, suspense and history, but I also love Gabriel Knight for it's more serious, mature, darker, and supernatural themes!
I'm gonna have to say both...