Why do Electronic Arts games for Genesis (Mega Drive) have a different cartridge size?

EA originally reverse-engineered the Genesis and made their own carts.

When EA inquired about publishing its games on the Genesis, the executives felt their proposal would be met with open arms.

Instead of embracing the logic in EA’s proposal, Sega of America president Mike Katz had other ideas. Sega wanted to emulate the Nintendo licensing agreement system, leaving little to no negotiation room for third-party publishers.

The discussion went back and forth for nearly a year, until a Sega executive boldly told Bing Gordon, “If you want a different deal you’re going to have to reverse engineer the system, aren’t you?”

Sega had thrown down the gauntlet, and EA gladly picked it up. Under the guidance of its legal counsel, the company gave two of its most talented engineers the green light to attempt a clean room reverse engineering job on the Genesis.

...EA’s hardware group built several reverse engineered development systems. Unbeknownst to Sega, EA ramped up production on several Genesis games.

Sega was caught in an uncomfortable position. If EA went ahead with its licensing program, the console manufacturer would be losing a significant portion of the profit that traditionally comes with the territory. EA could essentially reach out to other publishers and offer better returns and cheaper manufacturing costs than Sega was willing to do.

In exchange for agreeing to join Sega’s licensing program, EA would be allowed to manufacture its own Genesis cartridges, could make as many games as it wanted, and received a more favorable royalty rate.

source: http://bluetoad.com/display_article.php?id=773681

Complementing Cory J's answer, after some research, I found that the cartridges really have different PCB sizes.

According to this source (2nd answer), EA games PCB were slightly taller and harder to open:

Madden 93 "guts":