I own both, and ride them both regularly!
I currently have the Big Dummy set up with a 29" front wheel and a 26" rear, both with Schwalbe Big Apples, 2.35". It is more of my "road" cargo bike. It's my around town grocery getter, utility hauler, tourer, and commuter. Before I got the BFD, it also saw plenty of time on dirt, collecting wood, hauling trail tools, and camping. I've had it over 8 years, and it is my most reliable bike.
The BFD is mostly the stock setup from Surly, with Jones H bars replacing the stock bars. It is my off-road RV and trail maintenance tool hauler now, and more and more a fun alternative to a "short" mountain bike if I know I want to take singletrack home from the store. It is also my winter cargo bike. I've had it almost a year, and have yet to have a problem with it yet.
As far as cargo goes, they are almost equally capable. The BFD is noticeably stiffer with heavier loads, I think I would trust it with more weight than the BD. But, we are talking about 150+ pound loads. But, if you load either one poorly, you pay the price with poor handling, just like any bike. If you are looking at hauling loads off road, the BFD adds a lot of peace of mind. The big tires soak up a lot of bump, cushioning you and the cargo. I've found the BFD handles any bumpy trails when loaded better than the BD, though the BD does just fine on smoother gravel, and has seen plenty of singletrack before I got the BFD. Both have been airborne a few times now, though the BFD handles loaded landings better than the BD.
The BD will always roll faster and be less fatiguing, loaded or not, but if you air up the tires on a BFD, it isn't much slower. I typically keep 10PSI front and 15 rear, unless I'm hauling anything heavy. even aired up, the ride is noticeably smoother on the BFD. The BFD has the same "weird" handling characteristics as a normal fatbike, though they are a tad muted by the long wheelbase.
Overall, by the sound of it, and in my opinion, a Big Dummy would do you just fine. It'll easily haul everything you want to carry, it can handle a fair bit of offroad, and it'll last forever if you take care of it. It uses pretty standard parts, and is about 10 pounds lighter. However, keep in mind, you can build a fat wheelset and a 29" wheelset for the BFD, which, combined with a stronger frame, makes it much more versatile. It'll do everything a Big Dummy does, and then some. Fatbike parts are getting more common. Plus, while a Big Dummy gets some attention, the Fat Dummy takes it to a whole new level!
If I had to chose one? I would pick the BFD. If I broke the frame on my Big Dummy, I would probably rebuild it around a BFD frame, with 29" wheels.
Hope that helps!