(Usually not the EFF; more likely Software Freedom Conservancy or someone. EFF is more digital rights and privacy stuff, not copyright.)
A copyright holder can't get anything more from you by using the GPL. Infringement is infringement. The difference is that a company is usually happy to settle in exchange for a properly paid license, and an open source hacker instead is happy to settle in exchange for complying with the license. You're always free to take it to court and pay the damages from infringement, but you're not going to end up with a valid license in either case, so you'll have to stop distributing the software.
The actual difference, probably, is that you're a (moral) competitor of the open source hacker, and if you're not a competitor of the proprietary company, they have no interest in undermining the secrecy of your code or causing you to go out of business, even if the could potentially force that if they went to court. They're likely to consider "pay us a percentage of revenues" as a win condition.
Also, lawyers are not like Pokemon. You cannot beat the opposing team's lawyers by having more stronger lawyers. You can certainly lose by having bad lawyers, but you can only be guaranteed to win by being in the right.