The sonosubs are basically a sealed or vented enclosure in a different shape. They would certainly be quicker to build than the tht, but depending on your woodworking skills, a basic mdf enclosure may be within your grasp as well. As for WAF, only your significant other can tell you, but in my eye, sonsosubs, finished with the right covering, are aesthetically pleasing. I did consider a sonsosub at one time.
The tht(lp) will have higher sensitivity and lower distortion, due to the horn design. They are more challenging to build, however, BFM's plans are very detailed, relatively fool-proof (if followed to the letter) and geared towards minimal purchase of power tools. They're probably more challenging to finish to waf standards, especially the larger sizes.
As for use outside, the non-"lp" version of the tht is more cube-like and would seem less precarious to move than a sonosub. Neither design is really suited for outside events though.bThe THT, in particular is optimized for indoor acoustics. If you really want to move it around, I would give up on waf and paint either of them with duratex. As I'm sure you noticed BFM has several horn designs better suited for outdoors, (and for transport!).
Hope my two bits helps.