I am planning to buy a 2 story house in AZ. The air conditioner is on the roof and it is a brand new. House has 2 types of AC vents as pictured below. First picture vents are only on ceilings and they make a lot of noise, second picture vents are located on walls throughout the home and they are super quiet. How to reduce AC vent noise?

Are you sure the square ones are on the walls? I've never seen that type of register mounted on a wall but commonly on the ceiling.

You are correct, images are in the opposite order... do you have any suggestion to reduce noise?

Is it air noise, mechanical noise or rattle noise?

Is it air noise, mechanical noise or rattle noise?
Air noise

Short of calling a air duct/vent professional, home depot has some products for you to consider,

Search Results for air vent noise reduction at The Home Depot (http://www.homedepot.com/s/air%2520vent%2520noise%2520reduction?NCNI-5)

There are more elaborate products also

Noise Reduction in Ducts - Paroc.com (http://www.paroc.com/solutions-and-products/solutions/hvac/noise-reduction-in-ducts)

Air Duct Noise Reduction | eHow (http://www.ehow.com/way_5547834_air-duct-noise-reduction.html)

Many options out there.

Depends on if you want to throw some money at the issue. I would guess the excess noise is due to a large volume of air coming out of the more direct ceiling trunk. An air balancer could measure the volume at every register and throttle down so that are getting too much volume.