The inside. If using flip open top boxes like I do you can't read the label when the box is opened.
For resistors I don't label every compartment, I label the X axis and the Y axis. Eg:
10R, 100R, 1K, 10K, 100K, 1M - along the x axis
10R, 22R, 47R - up one side of the Y axis.
For the capacitors I couldn't lay them out in decades as I don't have full decades, so I left them in their labelled zip seal bags with the loose ones in the tray underneath. Eventually if the bags empty I will move the label to the inside of the compartment.