Or not: depending on how you feel about backflushing, it may be about even.
If you add a Tornado Tube to your Squeeze, you can leave the syringe behind - I haven't weighed it other than to put the Tube in one hand and the syringe in the other, but the syringe feels heavier. With the tube, you can securely screw a bottle on both ends of the filter, and backflush by turning it upside down and squeezing the clean bottle to force water backward through the filter. So, you may save an ounce or two by adding the tube and leaving the syringe at home.
With the Mini, you can't attach a bottle to the clean end, so (unless you're willing to hope the thing won't clog in the field) you have to pack along the syringe - and the Mini plus syringe feels about the same weight at the Squeeze with Tube but no syringe.
Now that we've totally overanalyzed that...