I still found Pulp Fiction more enjoyable overall, although there was more to the story of Forrest Gump. As far as their popularity in pop culture at the time (and especially in the long run), I think Pulp Fiction beats out Forrest Gump.
At the very least, Tarantino should have won an Academy for Best Director IMO. You could make a case for his directorial of Pulp Fiction being a more impressive feat considering it was only his second full-length feature film and the number of filmmakers who can make a classic film like Pulp Fiction in only their second effort (third if you count My Best Friend's Birthday, but that one shouldn't really count) are extremely rare indeed.
Hard to say at that time since I was like 1 or something, but Forrest Gump and Pulp Fiction are two completely different types of genres and although they're both good, Forrest Gump has Pulp Fiction beat. Pulp Fiction was not innovative, a lot of what Tarrintino does, in fact most of it, is taken from other movies and jumbled up into Pulp Fiction. It was unusual for it's time and action packed. However, Forrest Gump masters all of the practical Hollywood techniques that most movies use and what's unique about Forrest Gump is that it has so many parts to it, that it can almost be a bunch of movies jumbled up into one, except they're so smoothly connected that you don't even notice it. No movie has ever done that, past or present. To be honest I've seen more pop culture references to Gump than Pulp Fiction.
I'm not sure if I'd give him best director, it's hard to call that one. I will say that the academy awards tend to not give awards to the younger guys in the industry.