I think that's natural. The reason being is that with straps, all you have to worry about is pulling and receiving, whereas without straps, you have to add the element of grip and grip strength. Most people I know have a higher snatch number with straps when compared to their sans-straps snatch number.
If you want to try to close the gap, then maybe grip strength in the snatch grip might be your issue barring any considerable deviation in form between the two scenarios (e.g., I once saw a guy that had trouble with an early arm bend, but with the straps, he did just fine). You can work on no-hook grip snatches to work the element of grip strength, along with other execises without the hook grip -- cleans, deadlifts, and pretty much anything you normally hook grip on.
I hope this helps you (and I hope I'm right).
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.