Your question is kind of like asking which religion works the best. Everybody has an opinion. Many around here have adopted the 5x5 and the dual factor training theory. This is more strength training oriented. But, as you know, there is a correlation between strength gain and muscle gain although not in all cases (ie. Increase in neuromuscular coordination yields increase in power output without hypertrophy).
Zatsiorskys book, The Science and Practice of Strength Training is phenomenal. It outlines the difference between dual factor and supercompensation or single factor theory. Zatsiorsky clearly points out that hypertrophy is a supercompensation process. Dual factor was developed to address neuro-muscular training. More frequent workouts train your muscles to contract harder. Hypertrophy is a side effect from the protein break down under tension.
Sets of 8-12 will recruit more muscle fibers, including the highest threshold fast twitch fibers used in sets of 5. However, these highest threshold fibers wont fire at their optimum rate and therefore wont get as trained to contract as hard. Hence, 8-12 rep sets wont increase your low rep max nearly as much. However, these sets will recruit more fibers, exhaust more energy resources (creatine phosphate and glycogen), and break down more protein. The supercompensation set for set will be higher IMO with sets of 8-12. Some have attempted to increase their mechanical work load in low rep training by doing higher sets. Ie. 5x5 = 25 reps at a higher weight than 3x10 = 30 reps with a lower weight. Hence, the mechanical work with 5x5 is more than 3x10. However, I would bet that the muscle damage and energy depletion is higher with the 3x10 and the fiber recruitment is greater too. So, some have another perspective on the optimum rep range.
Personally, at my age and experience level, sets with reps lower than 8 are too taxing on my connective tissue. So, thats another consideration. You can periodize your workoute.g. hypertrophy phase sets of 8-12 for 4 weeks, strength phase sets of 5 for 4 weeks, power phase sets of 3 for 4 weeks, recovery phaseactive rest 2 weeks. I personally dont care for this as my primary goals is muscle growth, not maximizing my lifting numbers.
Then theres the volume and frequency aspect. Which is the best split? How frequently should you be hitting each bodypart. How many total sets per bodypart?
To answer your question, the norm right now for advanced trainers such as yourself is to train each bodypart once a week with 12-16 sets for legs, chest, back and 6-9 sets for bis, tris, calves. If hypertrophy and not strength is your goal, then this works fine. It probably allows more rest than necessary, but error should be on the side of rest. Research shows that advanced trainers can take 14 days off with no loss in muscle mass or strength, so waiting 7 days to train a bodypart again is not going to cause atrophy. I would never recommend this for strength training because you lose the training effect (ie. Coordination) rapidly. Repeated exposure is more important for strength. Can you do 3 on 1 off? Sure, if you control volume, then you can recover and do this split. I personally do it from time to time because I love training. But, at your level the norm is to allow more recovery to the joints.
This is a typical modern split: 1. Chest / bis 2. Legs 3.rest 4 Shoulder / tris 5. Back 6. Rest 7. Rest.
Id recommend trying something different and see what happens. Also, training naturally is different. Id decrease volume from the above mentioned if no gear is being used. That much volume is just not necessary and is counterproductive for a natural trainer.
Just my $.02
