Define gearing for me. If you are looking for the correct answer that's significant.
I'm thinking the other responders are referring to the same number of sprocket teeth as being the same gearing. If that's your definition of gearing, they are right. A larger wheel will definitely go faster.
Traditionally, bicycle gearing has used the concept of "gear inches". Gear inches = chainring teeth divided by rear cog teeth times wheel diameter in inches. That adjusts for wheel size so, just as your mechanic said, equal gearing will produce equal speed.
The elephant in the room when discussing bicycle speed is the motor. If you were to put a Ferrari transmission into a Yugo do you think it would go 150 MPH? Of course not because the Yugo doesn't produce enough power. Bicycles are the same. Once you get over about 15 MPH, most of your energy is going to overcome air resistance. You need power to do that regardless of your bike's wheel size or gearing.
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