I have no experience with the Triumph, but plenty on the Wee.
Mine ('06, 37,000 miles) has been dead reliable. It corners like an angel and has a silky transmission. Once you deal with the squishy factory seat, it is all-day comfortable. It gets excellent fuel mileage. It is not a dirty bird; once things go beyond roughish gravel the weight and the gearing make it readily apparent that this ain't no trials bike. However, up to that point, it is superb. If I were to use it for the rougher stuff, I'd likely mess with the sprockets to get more grunt.
There a few farkles I would not do without. The Madstad windscreen mount makes the ride very comfortable in all sorts of weather. If you are taking it into rough terrain, crash bars will save you tons of money in plastics. A skid plate is a must.
I added a set of toothy IMS-copy footpegs and bar risers, which make it more tractable standing up.
Once you get around the Darth Vadar looks (and you should be riding it, not looking at it,) it is a very well-mannered and comfortable machine. Your choice will depend on your personal taste, but I don't think the Wee has many bad points.