The lift less and more reps to cut is complete BS IMO. The entire philosophy of muscle building is thrown out the window if you apply that to your workout. If you're lifting less weight, but doing more reps, all you're doing is making yourself tired. You're not stimulating your muscle by lifting less weight if it has previously been adjusting to lifting heavier weight. The goal is to lift heavy weight so you will train your muscles to adapt to the weight, and by constantly creating a weight overload, your muscles will HAVE to adapt to the new weight, which creates muscle growth.
My routine looks like this:
1 warm-up set of 8 reps
1 set of 6
1 set of 3 (real heavy here)
2 sets of 4-6 (usually about 5 lbs lighter than the 3 rep; looking to go to failure in this range on the 2nd set)
By starting with a warm up set, you get your muscles ready for the heavy weight. The 1st set of 6 should be fairly heavy, again letting your muscles adapt to heavy weight (you wouldn't just jump straight from benching 135 to 300, you might injure yourself). The set of 3 is the set that is going to trigger your muscle into overload, and the ensuing 4-6 sets, even though 5 lbs lighter, forces your muscle to work almost as hard as it did on the 3-rep set, and really programs your muscle to adapt itself to an ever-increasing workload.
I just don't see the point of lifting lighter weight in any circumstance, unless you're going through an injury. Even if you go to failure on a 12-rep set format, you're going to failure because your muscles are just tired, as opposed to going to failure on account of weight stress. Ever notice that if you do a 3-4 rep set and go to failure, you can always wait about 5 minutes and do a 12-rep set with the same amount of weight that you could do with a fresh set of arms/egs/chest/whatever?
If you're not stimulating your muscles, you're not getting stronger. If you're not getting stronger, you're not building muscle. So if on a cut, doing a high rep set format, if you lose weight, a lot of it may be muscle. You might as well not lift weights at all. Jared from Subway lost a lot of weight, but he still has no muscle definition because he didn't lift weights. Your results may be similar if you don't lift heavy on a cut cycle.