Speedo Gear, or Re-code??

If I were to change the gears to 3.42, or even 3.73's, will I have to change the speedo gear in the trans, or get the computer adjusted for the new gear ratio. I hear different things from people in the business, GM tells me to change the speedo gear, and don't worry about it, and my diff guy tells me to get the computer re-coded for the new ratio? Well, which one is correct?

GM = $5

Diff guy = $100 -$200