SEA did sue PK, but not "naturally" because PKZip was faster and free (actually, PKArc and PKZip was shareware, as was ARC by SEA). SEA sued PK because it maintained PK lifted a lot of SEA's source code verbatim and used it in his software. In other words, it was about copyright violation.
The suit was settled under undisclosed terms after an expert witness testified that, indeed, PK did lift SEA's code.
Ironically, most members of the geek culture sided with PK because of the image spread by people who personally disliked Thom Henderson, the founder of SEA. The image was purporting that a big business was suing a small guy. In reality, SEA was a small business (essentially just Thom Henderson himself). The flack it received from the geek public was quite undeserved.
By the way, I can no longer remember the name of the expert witness, but long before the litigation I communicated with him on the 80XXX echo of Fidonet. I was always very impressed by the depth of his knowledge on the topic (which was assembly language). I am also convinced of his peronal and professional integrity. In other words, I believe he was a genuine expert, one whose testimony I would accept without hesitation.