Thats the ongoing discussion when it comes to the design on a t-shirt. What to put on the front, and what to put on the back. It depends on source of the design. Is it for an event? A function? Company dress code? In that vein, its best to have all of the design on the front of the shirt, and a minimal (if anything at all) on the back.
This is further reinforced when considering promotional or self-promotional t-shirts. You want the most vibrant part of the design on the front of the shirt. The reason being is you want the shirt to initiate conversation. As you approach someone, they will view your shirt, and if feel comfortable enough doing so, will compliment the shirt. This opens a channel of conversation and allows you pursue the conversation to perhaps a sales pitch or at the very least an opportunity to market yourself and your company or organization to which you are representing.
As for the back of the shirt, this can ben extremely useful in displaying information concerning the company or organization such as contact information via phone or email. Think of yourself standing in line at the grocery store, bank, post office. Or, walking around a crowded venue where someone might be walking near or behind you in which they'll have ample opportunity to see and take notice of your business or organization and possibly tap you on the shoulder for more information.
In summary, if your best design is on the front, and its good enough to prompt a compliment from someone facing you, you'll already be facing them to continue a conversation they initiated. If you best design is on the back, many people are no so inclined or comfortable with tapping you on the shoulder, a perceived intrusion into your personal space. Keep the god design on the front to initiate conversation, and informational content on the back.
Advertise yourself.