D3 will give you more power, but it will also use more gas. You shouldn't need to use D3 unless you are going up a steep hill (to keep the transmission from constantly down shifting and up shifting), or towing, for the same reason. If you push the accelerator down, the transmission should downshift on it's own, to give you more power (for passing). I certainly wouldn't ride around in D3, because that would cause the engine to run faster, and hence burn more gas.
1992 Accord EX, sold after 12 years
2003 Accord EXV6, present car