The second drawing (arduino_forum.png) implies a common cathode LED where you are supplying positive voltage to the three LED anodes and then you have bussed the single cathode to three pins on the driver. So you have no distinct control over the three LEDs anymore, they all act in unison. On the plus side, you can sink three times as much current as you are using three driver pins on the IC, assuming the LED can handle it. Since all three LEDs inside the LED package are always going to be on if any of them are on, you are going to get white or something like white, unless all three driver pins are fully off. This is not likely what you want. On the other hand, your first schematic (arduino_1_sch.png) will work fine as long as it is a common anode RGB LED. You will want to use 16 of them and occupy all 48 channels.