First, let's compare the sizes. Type 055 is about 590 feet long and 65 feet wide with a maximum displacement of about 13,000—14,000 tons.
Source: Popular Science
The Zumwalt, on the other hand, is a much larger ship at 610 feet long and 81 feet wide with a maximum displacement of about 15,656 tons.
Source: US Navy
In regards to propulsion, Type 055s have four QC-280 gas turbines, each providing about 23-28 megawatts of energy. This large amount of energy may one day power railguns or other future weapons systems.
Source: globalsecurity.org, The Diplomat
The Zumwalt, on the flip side, has two Rolls-Royce MT30 gas turbines, providing the ship with 78 megawatts of energy, including 58 megawatts in reserve. This reserve power may also power railguns or high-energy lasers in the future.
Source: The War Zone
In terms of stealth, Type 055 has an enclosed forward deck, main mast and bow, with the latter hiding the anchor and other equipment. But its hull and superstructure are fairly conventional.
Source: The National Interest, The Diplomat
The Zumwalt, however, is stealthy from the bottom up, including enclosed gun turrets and sensors.
The Zumwalt's "Tumblehome" hull and superstructure "significantly reduces cross section and acoustic output making the ship harder to detect by enemies at sea," according to the US Navy.
Source: The National Interest
As for radars, Type 055 uses X and S-band radars, with the former being used to track smaller and stealthier targets, and the latter being used to track targets at greater ranges.
Source: The War Zone
But the Zumwalt only has an X-band Spy-3 radar. It was supposed to have a similar dual-band radar as Type 055, but the S-band radar was cut to save costs.
Source: The War Zone, US Navy
And for armament, Type 055 has 112 Vertical Launch System cells, each cell having a diameter of about 2.8 feet.
The VLS tubes fire HHQ-9 surface-to-air missiles, YJ-18 anti-ship cruise missiles, CJ-10 land-attack cruise missiles and missile-launched anti-submarine torpedoes.
Type 055 is also equipped with an H/PJ-38 130 mm main gun on the bow, and H/PJ-11 and HHQ-10 close-in weapons systems for last minute defense.
Source: The Diplomat, The War Zone
But the Zumwalt only has 80 VLS cells, each of which have a diameter of about 2.3 feet.
The Zumwalt VLS cells can fire Tomahawk, Evolved Sea Sparrow, and other guided missiles.
It's also equipped with two 155 mm Advanced Gun Systems on the bow, and two Mark 46 close-in guns which fire 30 mm rounds. Rounds for the AGS are so expensive, about $1 million apiece, that the Navy doesn't have any and has no plans to buy them, rendering the deck guns effectively out of service.
Source: US Navy
Ultimately though, the two destroyers will have different mission sets.
Type 055 destroyers will focus more on air defense, anti-submarine missions and protecting carriers, which is why they have more VLS cells and a longer range than the Zumwalt. These mission sets, along with its large size, are why the US has even classified the Type 055 as a cruiser.
Although analysts say the Zumwalt is ultimately more powerful than Type 055, the US destroyer is more of a land attack ship, designed to deploy close to enemy shores and fire its large 155 mm guns like old battleships — if they ever get ammunition.
This also explains why the US only has plans to build three Zumwalt-class destroyers, and China plans to build about 12-24 Type 055 destroyers.