Well, even Bergkamp & Giggs played different role. Bergkamp was primarily a striker and Giggs, a winger.
That being said, this is a great face-off. Both are beyond legends in their respective clubs (Arsenal & United), both are surely amongst the 10 greatest Premier League players ever, lots of individual honors for both of them ect...Giggs was more of a defenders' nightmare while Bergkamp was more prolific. Giggs won more trophies and played more matches while Bergkamp featured in a World Cup.
Well, I prefer Giggs over Bergkamp personally but I respect your decision. Giggs had better pace and dribbling skills while Bergkamp had a world-class touch and finishing. In fact, many person surely prefer Giggs over Bergkamp and surely many prefer Bergkamp over Giggs. It's a close one - so I'll leave this one, open to personal choice.