Everyone realizes these birds are very difficult to tell apart. The main difference is size, but individuals are variable, and size is the most difficult character to judge properly in the field. Said another way, size is the most frequently misjudged field character in birds. It's almost purely a comparative feature, and if you have nothing of known size to compare it to, you should not rely upon it.
Size can be inferred from speed of wing beats, with smaller birds flapping faster. But then speed of flight varies with conditions too – wind direction and the purpose of the bird's flight, for example.
HABITAT is a great clue. Chihuahuan Raven prefers wide open, flat country with scattered bushes and lots of grass or open ground. They are not normally found in hilly canyon country. So unless your area is in the far eastern or northern parts of the circle, you are unlikely to encounter the species.
BEHAVIOR is moderately useful. Chihuahuan Raven is more likely to be found in large winter flocks, roosting and feeding in groups that can number over 100. They are much like crows in this regard. But if it's a feeding concentration, such as at a dump (there is not one in our circle), both species can be found in the same large flock together. And sometimes groups of 20 or more Common Ravens will gather to feed in fields or frolic in the updrafts on a mountain peak.
FIELD MARKS for Chihuahuan Raven include a more rounded and less wedge-shaped tail and a shorter bill with the culmen curving down to the tip just beond the nasal bristles. Common Raven has a very wedge-shaped tail (you have to see it well from below, such as in soaring behavior) and a culmen that continues horizontally for some length beyond the end of the nasal bristles before dropping down to the tip. Common also has longer wings. If it's windy, the ruffled neck feathers of a Chihuahuan Raven will show bright white bases, but the pale gray bases of Common's neck feathers can be misjudged as being white.
VOICE is good. You can sing the call note of a Chihuanhuan Raven, as it is nasal and tonal. Common Raven's voice is extremely variable but is lower and more croak like, usually descending and not on a single tone.