I've had 2 FJR's and 2 Yammy boxes and now have a Givi 52 mounted. The Givi BY FAR is built better. Superior locking mechanism, both on the trunk and mount. Less wasted space. The Yammy case wiggles with the slightest touch where as the Givi is solid as a rock. Holding 2 full face flip-up helmet is a real plus. I'm not sure why Yamaha wasted so much space with the rear portion of the case.
They are both very close in price, call up Gary Mccoy in Fargo order your Givi for about 10% less than the best web pricing.
On a second note, I'm rebuilding the front forks and changing springs. Last night I put 3 25 lb weights in the trunk and couple 2x6's under the header (only holding up about 7 lb's) It worked great. I wouldn't trust that plastic Yammy case to hold much more than 1/2 of that.
My wife likes both of them without the back rest. We've had the yammy case with and without the backrest.
Personally I like the looks of the yammy, but the function of the Givi is much better.