Can you describe the noise? Is it water rushing type? Whoossshhhh? Or are you getting a sppptttt sppppttttt air bubbles spitting out? Or is it more of a high pitched "singing" noise? Mmmmnnnnnnnggggg?

When you replaced the faucet, did your fixture have shut off valves below that you used, or did you have to use the whole home shutoff and drain all of the pipes? What brand are your fixtures and what type (copper, CPVC, PEX) are your pipes? What age is your home?

The noise is a rushing or whooshing sound. No spptt nor bubbles nor high-pitched noise.

The fixture is hooked up to individual shut-off valves below. Don't know the brand of the vessel faucet as I bought it on ebay and it's made in China. The tub faucet is Moen Monticello, single handle.

We have copper pipes but that isn't the problem. The noise is definitely in the faucets. I just put my head under the counter and the vessel faucet is loudest above the counter. The tub faucet's noise almost becomes normal when the shower diverter is turned on so I think the noise there is also in the faucet and not the pipes in the wall.

The pipes on the vessel leading to the turn-off valves are flexible metal (bought at Lowes). We had to put a 20" and 16" together so they would reach the faucet (which is also a single handle) from the shut-off valves.

We built our house in 1999-2000 and moved in the end of January, 2000. Complained to the contractor about the tub, but, true to most contractors, nothing was done (this was after he got all payments. We hadn't turned on the tub faucet for bathing as it is the guest bathroom so didn't notice it until a month or so after moving in).

Hope this gives enough info. It's a mystery.

As a plumber who does a lot of new construction and warranty service work I have had to deal with issues such as this before. Most of the time it is a characteristic of the particular faucet that is installed. What is noise to one person the next person sometimes doesn't even notice.
The little screened opening on the sink faucet where the water comes out of is called an aerator. It can be unscrewed off of the faucet, usually by hand. Try running the water with this taken off, and see if it makes a difference. Careful, water will want to spray out in a wide pattern rather than in a uniform stream down. If it does make a less noisy difference, buy a different one from Home Depot or another store and see what happens.
The tub faucet noise could be coming from the spout. I've seen some designs that are more noisy than others. Try changing the tub spout to a different one and see if it makes a difference.

Thanks. I'll give it a try.

I was curious if you ever solved your problem? I know this is many years ago, but I am in a new construction home, 6 years old and having similar issues. I was curious as to if the only way to resolve is change out the faucets that do it.