In terms of the strength or hypertrophy game how many muscles you train on a day depends on how you train.
HIT: It's over quick, you can train a lot of muscle groups, you don't have to train every day. It is neurally draining, most people can't hack the "intensity", your form has to be perfect on every single rep (injury chances higher when pushing the boundries of failure).
Fullbody: Cover all the muscles, good for sports, good for big movements, increases hormone release, increased level of frequency. Usually end up being long sessions, mentally and physically draining, can play to your strengths rather than fixing weaknesses.
Upper/Lower: Balances leg vs upperbody, good frequency, increases hormone release, can train opposing movements (more efficient), allows time to be spent on weaknesses, is what Westside do (kinda). Tends to focus on only smaller number of exercises, can be mentally and physically draining, a lot of people can't hack leg workouts twice a week.
Push/Pull: ditto upper/lower but can be better for balance between muscle groups.
"Splits": great for targeting weak points, can provide good overload, usually more hypertrophy focus, can't be high frequency use cummulative fatigue (good and bad), can tend to focus on upperbody development, body isn't a series of body parts so exercise selection has a lot of overlap (which can lead to overtraining of some supporting muscles).
So none are perfect and it depends on what you are trying to achieve. I think the most versatile are the more frequent training types that cover a lot of muscles (U/L or PU/Pll) as they can be designed to give you strength, hypertrophy, both or built around sports. They also allow for greater hormone and frequency which will ultimately allow more growth long term. Although my points on hormones may be off as Kraemer has some new work out that shows T levels don't change. | 
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