The NFL never bothered to investigate the kickers and find any potentially incriminating texts and calls to the ballboys. Also, the kickers weren't dicks to Goodell and the NFL and called them liars in public. (See earlier post about Brady being punished for basically being a dick in Goodell's eyes)
Also, not super relevant, but you could argue that the kickers were going from having control over their footballs to having to use brand new balls, while in this case, QBs were given way more control over their footballs in the past, but still Brady screwed around with them. Since Brady and Manning were two of the staunchest folks arguing for QBs being able to mess with their footballs during home games, Goodell may think that Brady got the rule changed just so he could mess with the footballs more.
Hence what it feels as though Brady is being railroaded here.