Day One: Lower Body
Training must be varied and cycled. Please, don't get stuck with the same routine day in and day out. If you train all your body muscles at every session, this guarantees zero muscle growth. This is without even mentioning boredom and lack of enthusiasm.
At each single training session you should concentrate in a particular body part, for example breaking your workout week into upper versus lower body training. This will result in more intense training sessions. With split-based routines, there's much less general fatigue occurring.
Day Two: Upper Body
Needless to say, if you only have two muscle groups instead of the entire body to worry about in a given workout, those two muscle groups are going to receive concentrated attention, which will result in better results. It's virtually impossible to give each muscle group the concentrated attention of a split-based workout when attempting to work the entire body in a single session. With a split-based routine, you can get an intense, extremely high quality workout in as little as a half-hour. You leave the gym feeling fresh, motivated, and with a feeling of accomplishment. Don't underestimate the importance of this benefit. The more you look forward to going to the gym, the better your workouts are going to be and the more you're going to accomplish with respect to your goals.