Private military company vs Navy Seals

SEALs.

depends on way to many factors from weapons, intel to who comprises the private military company.
if it is simply a matter of  resources than U.S. wins they are able to escalate past what a private company can get it's hands in. 
if it is a simple skirmish with both sides have equal weapons it becomes a toss up depending who comprise the private company military.

some private groups hire retire or ex navy seals but if there are not seals all day baby

Gotta go with seals, though depends on how the Private Military is.

Navy Seals 90% of the time.

Seals . Trident

Depends on what PMC it is home slice... but more than likely the Seals win
 
But If they have this guy.... 
 

The Navy Seals dominate here.

you guys realize that their is no set personnel for the private company hence no idea who compromises them?
 
the video is amusing but not a deciding factor aside from the navy seals other military personnel are also given basic knife fighting training. 
The Marines are also taught knife fighting termed bull dogging similar as the above only difference is they are not as enthusiastic as the guy who is hamming it up for the camera and some laughs.
 
if the Private military guys comprise random civilians than they lose if they are comprised of basic military personnel they lose.
if they are comprised of Marines grunts or recon, Army recon, or even Navy Seal that is an equalizer and possibly a game changer as well