You may say that I am comparing apples to oranges here, two vehicles that are totally different.  But in 1985, these two vehicles were directly competing for your compact-car dollar.  I owned a Honda Civic, and so did my friend Tim.  After driving and working on both of these cars, along with my Chevette, I have put together some conclusions about the strong points and weak points of the two rides.
 

Body / Paint / Structure
When it comes to the body, Chevrolet definitely wins this hands down.  The Chevette has a pretty tough structure.  This can be felt when closing one of the doors.  A solid thunk is felt, when shutting one of the 4 doors.  While the Chevette does not have a frame, check out these stamped-steel rails that run the length of the body and give it such a firm structure.
 

Something can definitely be said about the fact that this car is almost 20 years old, and the paint is only now starting to look bad!  The car has only light surface rust in places, which is probably due to the fact that the paint is dead, and not protecting the metal anymore.  A good sander, and my spray gun ought to solve this problem!
 

Early Honda's from the seventies and eighties were notorious for having poor quality paint and bodywork.  Both the Honda I owned, and the one that Tim owned had problems with the body's structure de-forming over the many years of driving.  Both of ours had problems with the doors and tailgate not aliging properly.  The poor paint jobs these cars had compounded the problems that these cars had with trapping moisture in nooks and crannies, and causing rust-out.  Honda's frequently rusted out around the rear fenderwells, rockerpanels, and quarter panels, floorboards, etc.  Now this is not to say that a Chevette will never have rust holes in them, but very few eighties and earlier Hondas remain on the road, in comparason to Chevettes simply because they rusted out, and wouldn't pass inspection.  This additional structure though adds to the weight of the Chevette, and thus reduces power to weight.

Engine
This is a toss-up.  Certainly the Honda engine can be more reliable, and it didn't have anywhere near the problems that the Chevette had with internal componets failing like head gaskets, camshafts, and other stuff, but Hondas were certainly well-known for their cantankerous carburator setups that even the most skilled mechanics could not get straight!  The Chevette has a rather crude version of computer control on it that keeps the timing and mixture tuned up,and also simplifes the emission control systems.  The Chevette also gets high marks because even the early models that were built in the seventies had nice aminites like hydraulic valves that didn't need adjustment, automatic chokes, electronic ignition, and solid-state voltage regulators.  Honda did not install any these features on the Civic until it's third generation in 1984, and some were still optional, or simply weren't avaliable.  As mentioned on the previous page, the Chevette I own started on the second crank after it had been sitting for about 2 years.  Honda Civic's would rarely start on the second crank if they had been sitting just 12 hours.

The Honda engines must get counted for the fact that they stay tight for a long period of time, and don't burn oil or leak fluids as bad.  The Honda engines have also been much better at producing more power with a smaller, lighter package too.  The 1200cc Honda engine was producing 70 Horsepower, the same amount of power the Chevette's  larger, and heavier 1600cc engine was making.  A Civic with the early 1500, or later 1600 engine was truly fun to drive, since they started with 90 horsepower, and were eventually tweaked out to 112 HP.  Honda also gets good marks for their early CvCC engines.  These engines did not need any emission control equipment on them since they burned so clean.  In the eighties though, the Honda engines got increasingly complex as emission laws tightened, and eventually became way too complicated for the backyard mechanic to do anything more than basic tune-ups to.  This complexity led to all sorts of drivability issues like hesitation and hard starting, that most mechanics had a hard time clearing up.

Interior / Confort
This is something I must give to the Chevette.  The Chevette's dimensions are made with an American driver in mind!  The roofline is tall, the seats are big, and the back is actually useable!  Interior fabrics, while stark, were well made.  The Chevette also has sound insulation in many of the nooks and crannies, making them much quieter at highway speeds.