I'm at a loss for how to show that one pilot might be better than another in the cockpit.
Firstly, the easiest way to present a better pilot would be with Skills. As per the Core rules (where Drive is outlined in the Fate SRD):
A futuristic setting revolving around people in a space opera military might have Drive (for cars), Pilot (for starships), and Operate (for tanks or heavy military vehicles).
A player might seek further enhancement for her character in the form of Pilot-related Stunts; a player willing to trade one or more Refreshes for additional Stunts shows the commitment to a depth of focus in a Skill.
While you can use Extras as a basis for the Mecha armour, you could benefit from some basic (and free) guidelines - such as those offered in respect of CAMELOT Trigger. The page outlines the basic concepts for creating mecha armour:
You can use these rules to build custom armour for your character, or as the basis for taking your favorite mecha setting and using Fate Core to adventure inside and outside the mecha
A fair invitation from those nice people at Evil Hat! As all Player Characters have a mecha suit, you don't need to use up their personal character resources to create them as Extras. The CAMELOT Trigger guidelines outline a suit supporting five equipment slots - allowing each player to create a personalised mecha to fit their concept.
More importantly than pilot A being better than pilot B in mecha 1, is how to show that Pilot A might be able to make mecha 2 an even match for mecha 1, when a mediocre pilot could not.
Per the CAMELOT Trigger guidelines, the internal systems of a mecha can:
give your character a higher skill level while in your armour, replacing the skill, although you may use the character’s skill if it is higher.
This allows for the scenario where you have a character with Great Pilot skills and another with Average. If their mecha both have Average Pilot support systems, then Pilot A can use Mecha 2 with Great Pilot skill, whereas the character might have optimised Mecha 1 for Fight and Provoke. Pilot B might have set up Mecha 2 with Good Pilot support systems, compensating for his weaker Pilot Skill, but Pilot B has better Shoot and Stealth skills - making him the more dependable option when infiltrating an enemy base.
Pilots Create an Aspect to give bonuses to the mecha
When it comes to running/playing your game, this absolutely would be the way to run things. You can have Pilot B using his Provoke skill to Enrage an enemy pilot and get him off-kilter and open to a smart Fight move on the following turn. A team can set up Advantages for the benefit of each other, creating free Invokes - say by blinding an enemy Mecha's sensors or binding their servos with undersea cabling.
If you mimic a movie like Pacific Rim, you could have one Pilot in "the drift" create the advantage and the other Pilot uses it to complete an attack.
While all this can come from your own imagination and using the Fate Core SRD as a guide, you might also consider spending a few dollars to pick up a setting like Apotheosis Drive X from Machine Age Productions or Mecha vs. Kaiju from WrightWerx. Also consider digging into the Fate Core Toolkit for ideas on Vehicles, Monsters and Scale - the last being important in dealing with massive machines and threats faced by tiny pilots!