Down, is that 1db coming from an educated guess or some published specs somewhere?
Almost universally, larger speakers of the same design (ie they're just proportionally bigger and that's it) will have higher sensitivity, and will go lower.
In this case, a 2x6 is a pretty damn small cab, which I wouldn't expect to get really above bedroom to coffee shop levels. A 2x8 as mentioned is almost 80% more cone area. I dont know if it's possible to figure out a sensitivity curve (ie if doubling area gives you 3 db, where do you hit 1db and 2 db?), but I would guess you'd get at least half of it in broad band terms, and possibly a lot more in the low end (where it's going to be most noticed).
So in real world terms, I wouldn't necessarily expect it to be perceivably louder, but I WOULD expect it to be perceivably fuller sounding. Having said that, I don't think the increase would necessarily be worth it depending on your aims and your budget. If I had the 2x6 and needed more volume for some things, I would be inclined to do a bigger jump to a 2x10 or bigger, and keep the 2x6 for home practice and very low volume situations. But you can get 2x10s these days that weigh about as much as 2 basses in hardshell cases. The added utility vs cost vs volume of anything much smaller than that is questionable at best. A 300-500w 2x10 can cover quite a bit, cost less than $500 brand new for a pretty nice one (or an amazing used one), and fit in the passenger seat of a porsche 911.
Of course maybe you already have a bigger cab and the 2x6 is just too small to be usable for you, in which case replacing it with the 2x8 might make sense.
BUT, the Trace 2x8 is rated 500w and is a pretty great sounding cab (although surely different than the MB, since it doesn't have a tweeter). It's got a bit of a vintage vibe without a tweeter, but it's also a 2x8 so it's still got plenty of highs. And if you used flats you wouldn't be getting anything from a tweeter anyway (not that was very usable at least). They're not exactly cheap though. But they are something like 28 or 30 pounds (maybe less?). And rated at 500w. So 2 of them could probably handle just about any bar or small club gig with a 300-500w head.