So I have been doing this for the last couple of months and here is what I have found.
The sets across method works great for any exercise as long as it's not the first one. For the first exercise I have found that there is no better way than pyramiding up in weight within a given rep range. I know that the traditional way of pyramiding up is lowering the reps while increasing the weight (15,12,10,8,5 for example) what I am talking about is picking a rep range like 8-12 reps and staying in it as you increase the weights from set to set. The reason I think this works better is because it really prepares your body for the heavier sets. It ends up serving as a warm up for your muscles as well as the nervous system. Plus there is still a good amount of volume there as you work up.
Now getting back to the sets across method. I have found it to work great for any lift. Barbell, dumbbell, dips, and chin ups, it doesn't matter. The overall volume is pretty high when you consider the total tonnage (sets x reps x weight ). I like to use either 4x8 or 3x12 as my set/rep scheme. For example if I am using 4x8, I will pick a weight that I can get for 8 reps without going to failure on the first set. When I can get 8 reps on all four sets then I increase the weight. This makes it much easier to select an appropriate weight as well as leaving a lot of room for progression (first workout you might do 8,6,5,5). It is much easier to gauge what weight you can comfortably do for 8 reps on the first set rather than trying to pick a weight that you can do for all four sets of 8 reps.
I think that combining the two methods (pyramiding and sets across) works better than just using one or the other. Another thing I like to do is limiting all of the lifting aids (weight belt, straps, wraps etc.) to only the first exercise. Here is what my last workout looked like:
Deadlifts: 6x4-6 pyramid
135x5 (warm up)
205x6
245x6
285x6
325x6
365x6
405x4
DB shoulder press: 4x8
35's x 10 (warm up)
50's x 6 (warm up)
60's x 8,8,7,7
Neutral grip pull ups: 3x12
BW x 12,6,6
Incline crunches:
3 sets with a 10lb plate behind my head.