Ultimately, the frame is the most important part of any bicycle the biggest issue in comparing the two is going with the one that fits you and your stoker the best. Next consideration would be how each one "feels" when you ride it. This is where these two bikes should be quite different.
The original Zydeco was a "one size fits all" entry level tandem with an open frame design. The open frame was phased out because, as you would expect, it was very flexible and handled poorly under all but very svelt teams. A mixte frame design was used on newer Zydeco tandems which stiffened up the frame and accommodated shorter stokers at the same time. The components are "best value" grade and good enough for light recreational use.
The KHS Sport, on the other hand, uses a time-proven frame design incorporating a head tube to rear seat tube internal tube that is well made and will give you predictable handling and control. However, it's a tank compared to the Zydeco. The components are not quite "best value" level but adequate for "comfort bike" riding, e.g., river trails and fun rides.
It all comes down to how you intend to use the tandem. Frankly, if you could swing a deal on a KHS Comp for about $1k you'd have a really great starter tandem that's superior to both of these models. The Comp is truly a great value given the quality of the frame, the better components, etc...
Bottom Line: The frame is the key. Make sure any tandem you're considering fits properly (getting a tandem that's too tall or too small isn't a bargain at any price) and gives both the captain and stoker a comfortable feeling ride.
Check out: http://www.tandemmag.com/classified
before you make your final decision. There are often times some great used tandems at very attractive prices for sale that can be found on this Web site.