Realistically, even if the supply tubing were 1/4", that would be MORE than sufficient to provide full flow and pressure from a faucet. Have you ever looked at how tiny the holes and water passages are in an aerator?
You clearly have some kind of blockage, either in the stop valves, the supply lines, or the fixture itself. If the "trickle" occurs for both the hot and cold water, then the blockage is almost certainly within the fixture itself. What is odd is that, from your description, this is apparently occurring in two different new fixtures: a bathroom faucet and a kitchen faucet. This makes me suspect you made the same installation error on both new fixtures. Did you apply any kind of thread sealant, pipe joint compound, or teflon tape on any of the connections? (If you did, you should not have.)
The way to find the problem is by the process of elimination. First, as John was hinting at above, make sure all your stop valves are fully open. Next, disconnect each supply line, put the end in a large bucket, and turn on the stop valve. You should have a forceful jet of water coming out of each supply line.
Next, reconnect the supply lines, remove your aerators, and turn on the fixture. You should have a fast and strong stream of water coming out of the fixture with enough force to splash vigorously in the sink. If you do, then the problem is with the aerators. If not then the problem is within the fixture. Are these single-handle faucets? It would make more sense if some foreign substance or object got into the single-handle valving. You may have to remove the supply lines, remove the aerator, and backflush the fixture with the faucet valves open to clear any obstruction in the valves. You'll probably want to take the entire fixture out of the sink and do this outside with a hose. Or you can try using compressed air, no higher than 60 psi.
