There are 3 key issues going on:
1. Appear equal... WHEN [condition] - the meaning is that the generally appear equal in size, but in one circumstance, in the air, they don't. In most of the answer choices, the sentence is composed as "appear equal in size when sitting on a branch or.." as opposed to the correct answer, E, which says they appear equal when they viewed in a specific environment, not enacting a specific movement such as sitting on a branch.
Second, I actually thought "appear equal...to each other" was redundant as "appear equal" generally implies between the two items in question.
2. The first clause is dependent, so the second clause must be independent.
C can be eliminated as we require an independent clause on either side of a semi-colon and C's structure is <dependent clause> + [semicolon] + <independent clause>
3. Due to Vs because of
A. appear equal in size to each other
when sitting on a branch or in a nest, in the air, the Common Nighthawk appears much larger
due to its greater wingspan.
B. appear equal in size to one another
when sitting on a branch or in a nest, in the air, the Common Nighthawk appears much larger
due to its greater wingspan.
C. appear equal in size
when sitting on a branch or in a nest; in the air, the Common Nighthawk appears much larger because of its greater wingspan.
D. appear equal in size to each other
when they are sitting on a branch or in a nest, in the air, the Common Nighthawk appears much larger because of its greater wingspan
E. appear equal in size when they are seen on a branch or in a nest, in the air, the Common Nighthawk appears much larger because of its greater wingspan.