First off, let me state that either of these philosophies will be of benefit. I will discuss some of the differences and will mention certain aspects that will work better for me but I don't intend to say which one or the other is better.
The training plan suggested by Matheny seems to make sense to me. Typically it seems logical to me that training rides should build up to be close to the actual competition distance (ideally, you would peak with a ride or a few rides that would actually exceed the race distance). However, it gets real difficult to find the time for these rides when you start getting over a century and if you're doing the traditional '10% weekly increase' training plan, you have a significant time period over which you're supposed to be doing these really long rides.
The one problem I have with both of these, indeed with most training plans, is the idea of a recovery ride. Why spend an hour on the bike (which winds up being at least an hour and a half by the time you get the preparation and post-ride shower taken care of) if your only goal is to NOT exert yourself?
Another problem I have is that the LaC Ultra occurs kind of early in the season (May 28th - 29th this year) so I really need to train according to a training plan; I can not rely on just riding around and coincidentally winding up with good fitness at the end of the summer like I did last year. I simply don't have the time to do a 3-4 month base build and 1-2 months of build phase. I'm considering two peaks this year, the LaC Ultra and RAO.
Currently, I have a training plan based on the traditional 10% weekly increase (specifially from www.ultracycling.com). I will do a volume peak shortly before the race, and then the taper. My intensity will come from short weekly rides, one consisting of flat speed, the other being hill work. Both of these rides are less than 50 miles. There will be two weekly volume rides: one ride that is about 30% of the week's long ride but is at a greater than race pace, and the long ride which is at race pace and will increase by 10% every week.
The problem with this is that in April, my long rides get into the double-century range. That's a lot of bike time, even for an unemployed slacker such as myself. One alternate that I know someone has used in the past is to just do a century both days of the weekend. This gives good overall mileage and also stresses the body for doing a century without sufficient recovery. That will be something to consider for RAO, but I think I'll be better-served for LaC by having one longer ride instead. The longer ride will also ive me a chance to get my nutrition plan ironed out. If I'm riding along I intend to do these rides non-stop as much as possible. that will also allow me to calculate my typical dilly-dallying time requirements.