I use a Madsen bucket bike multiple times per week, primarily to haul my two kids (one is 14 months old, the other almost 3 years old) to/from daycare and around town in an effort to use our car as little as possible. It's also great for grocery runs; the bucket holds quite a lot, and the bike operates very stably when loaded.
I bought this bike sight-unseen as a replacement solution for a kiddie carriage that the boys disliked traveling in together.
The bike was delivered fully-assembled in a gargantuan box, shipped direct from Salt Lake City where the company is located. Mine was part of a 'scratch and dent' special they were having on some bikes that arrived from the overseas manufacturer with cosmetic blemishes.
Prior to purchase, I did the requisite web research and came across the same totcycle review referenced above. (I also corresponded with Jared, one of the company's owners, over email and finally by phone to get my many questions answered before taking the plunge. He was very helpful and personable, and it was reassuring to be able to speak directly with 'the source'.) Regarding the totcycle review, I largely agree with that reviewer's comments and criticisms. As soon as I find the time, I plan on posting an in-depth Madsen review of my own on this forum.
I've only had the bucket bike for a couple months and have put less than 200 miles on it, so I can't yet speak for it's long-term durability. Only maintenance so far has been tightening some loose spokes, pumping up the tires, and fiddling with the alignment on the front disc brake -- which I can't seem to ever get quite right. So far no issues with the chain on mine, and I've definitely put some stress on it (taking decent-sized hills under load, giving my wife lifts home from work with both kids along for the ride, etc.).
If I were to make a prediction, I think the wheels may present troubles down the road if I continue to use this bike as heavily as I have been. They just seem too light-duty for a load-hauling bike. Also, the limits of 1x8 gearing can be an issue if you live in a hilly area like I do. Though the SRAM rear derailleur has performed well so far, before my legs became sufficiently acclimated to the work of propelling such a heavy bike, I was seriously considering adding more rings up front in order to expand the available gear range. This may be a tweak I make in the future (complicated by the presence of a good-looking and very utilitarian chainguard). I think it would be a good idea for the makers to offer this as an upgrade option.
Though this design won't be ideal for everyone, the Madsen has opened up a whole world of car-free kid-hauling for me and my family. I don't regret adding this bike to the stable and would do it again, especially since my two boys visibly -- and audibly -- take pleasure in going by bike now instead of barely tolerating it before in the trailer.
Hope this helps a bit. Again, I'll try to post a more comprehensive review when time allows.