I have used all 4.
Personally, I find the Ute okay, but not something I'd personally consider. Yes, it comes in nicely equipped at a decent price tag and it looks pretty attractive, but it isn't Xtracycle compatible and while it has a high volume design I personally found that it just isn't as robust as the others - I'd treat it as a high volume grocery getter, personally. It does indeed wiggle around a bit too much when loaded, I find.
The Radish is "okay" too. The frame they use is pretty nice (although as others have mentioned, the Radish is really just an Xtracycle conversion kit + bicycle, not a one piece unit)
Some big downers on the Radish though: There's only a single ring in the front, so the Radish will not be quite as good as the others if your area is *very* hilly. The new models also come with the hoodie bag instead of the freeloaders + snapdeck. The hoodie is not quite the heavy duty system that the standard kit is. Lastly, no disc brake mounts on the fork anymore - though the Avid V-brakes aren't bad, some people really want disc. I think the Radish is a good bike for someone who wants a high volume grocery getter, it's pretty nice looking, pretty casual oriented. Power users would probably be disappointed, but I like the Radish more than the Ute.
On the budget end of things though, one can purchase a good quality used hardtail mountain bike and an Xtracycle conversion kit and end up with a bike that is equipped with better cargo capability than the Radish or Ute for less money. I think it depends on whether you are willing to spend the time and effort on that.
The Yuba is pretty neat. It's a big heavy piggie, but it also totally outclasses even the Big Dummy in load carrying capacity. Yuba isn't Xtracycle compatible, but they're pretty committed to making decent accessories of their own (the go-getter bags are awesome!), I personally totally love the Yuba - but I wouldn't really want to choose this bike if it were going to be used for bike tours. It has a nice cruisery ride to it that makes it fun! Very lax handling, pretty upright.
Big Dummy is really nice. It is the second most cargo capable bike of the lot, and is the highest quality of the bunch. The Big Dummy is a top choice if you want a bike that rides really nicely at a wide range of load levels, I personally feel that it is easily the highest performer of them.
Out of them all, I would personally be inclined to choose either the Yuba Mundo or Big Dummy, depending on whether or not I really *needed* the 440lb + rider limit on the Yuba, or whether the 400lb total limit on the BD would be enough. 440 lbs of stuff is kind of really hard to pack onto something like a longtail though, I think you would have to be packing bags of sand and bricks to get that much weight before using up the available volume.
If you weren't bike touring or expecting a really light and svelte bike, the Yuba is all around fine. I enjoy riding it quite a bit, it's just a bit too piggy to want to take on 60+ kilometer rides each day in my opinion. Also, even though the Yuba is also all terrain rated, I have no doubt that the Big Dummy would be my preferred choice again if the riding became truly off-road.
So.. My logic path is kinda like this!
Need *lots* of weight capacity? Yuba
Want a bike that still classifies as performance? BD
Don't need the immense weight capacity *or* a performance ride, but still want a high capacity bike and don't want to pony for the BD? I'd probably purchase the Yuba over the Ute or Radish again, personally - sure, it's heavier. It also actually has a pretty comfy casual ride, and is going to be stiffer and more capable.
Lastly, if you really just needed the cargo bike and wanted to save money, an Xtracycle conversion kit and a decent hardtail mountain bike from a bike co-op or craigslist or what-have-you will be like a lower cost Radish with a better bag system and possibly a triple crank.