Hawkins is a Commander and Newley a Captain so wouldn't that make Newley the superior?

It depends on the Alliance's rank system, and the formality of the terms 'captain' and 'commander'. Both can be given as 'courtesy titles'. A person with the rank of commander can be called a 'captain' on the ship he commands. Also, in some armies, including the US Army, 'commander' is used to refer to the highest ranking officer of a particular unit. This probably describes Hawkins. His actual rank in the Alliance may be something different, but within the unit his is commanding, he's known as "Commander Hawkins".

From Wikipedia:

In the United States Army and United States Marine Corps, the term "commander" is officially applied to the commanding officer of army units; hence, there are company commanders, battalion commanders, brigade commanders, and so forth.

This wouldn't be entirely unlike Battlestar Galactica, where Commander Adama is the "captain" of his ship (prior to Cain's arrival), yet the the ranks are a mixture of naval and army nomenclature, basically as follows:

Officers:

* Admiral
* Commander
* Colonel
* Major
* Captain
* Lieutenant
* Lieutenant (junior grade)
* Ensign

Enlisted:

* Master Chief Petty Officer
* Chief Petty Officer
* Petty Officer (1st, 2nd Class)
* Specialist
* Deck Hand
* Recruit

Making things even more complicated, there are also Marines aboard Galactica, who conform more closely to the traditional enlisted Marine ranks. All of the Marines that have appeared onscreen to date have been enlisted, with ranks such as Private, Corporal, Sergeant, and Gunnery Sergeant. Unresolved is the question of whether the Marine officers would also adhere to the mixed rank structure (which sounds odd), or if they are strictly army equivalents (which makes no sense, given that the "Navy" ranks seem oblivious to there being any such distinction).

Translating this over to the Voltron universe, we see Keith referred to as "Captain" (a Galaxy Alliance CAG-type rank?), but with Commander Hawkins seemingly outranking Captain Newley. Given the fact that both Keith and Jeff command what are essentially air groups (in naval parlance), it's entirely appropriate for Keith to be addressed as such.

(Anyone recall offhand if Jeff was addressed by a captaincy rank on the Vehicle series, or not?)

Interestingly, the Devil's Due comics dealt directly with this very subject, with the former Colonel Hawkins -- in Galaxy Garrison's infantry-command apparat -- getting "demoted" to Commander, and reassed to a new naval command, the Explorer. Evidently the linearity between "colonel" and "commander" across the two service branches is somewhat parallel, despite the storyline's mention of Hawkins's supposed "demotion."