I got to where I am on BASIC lifting principals (heavy, low-med rep, compound movements). I would still continue to train this way if my only goal was to add strength, but since I am pretty strong at this point I switch my rep ranges up once a week and do the same exercises. I get stronger from the heavy days and bigger from the higher rep days. An alternative would be doing both, such as mentioned in the UHT program under the Articles section of the site. That combines both by doing 2 sets per exercise (1 in the 4-6 range and one in the 8-12 range). Because I'm lifting EOD and doing full body, I stick to 1-2 exercises per body part. Every set to complete failure, of course. I tend to agree with the people that say you only need to reach the point of tearing the muscle for it to regrow back bigger and stronger. I don't find that doing 3-4 exercises per body part with 3-4 sets each provides a better benefit in terms of hypertrophy than just reaching that "tear" point in 1-2 sets of failure.
The only argument I feel could stand against this is with legs. Being that we use our legs for so much on a daily basis, I've always felt that more "type 1" muscle fibers in the legs are stimulated through higher reps. I train my legs completely different than my upper body by just hitting a LOT of reps. I will throw light weights on the hack squat machine and bust out as many reps as I can until walking is next to impossible. I like the program I'm using above but I don't think doing 1 set of 10 squats is enough to generate adequate growth in the legs. thats my 2 cents though