Are there any advantages to the Mg 131, or is it just an inferior weapons system?
Lighter round, lower velocity, no ROF advantage. Seems like it kinda has nothing going for it.
Keep it in perspective. When directly comparing it to the other 1/2 in calibers it may be on the lower end of the totem pole in terms of velocity, trajectory, and rate of fire, but the German 13mm it still is launching a 590gr slug at 2320 fps (vs the US .50 cal = 705gr @ 2800 fps). It can still shred an aircraft easily enough. When I'm in German aircraft armed with a pair of them in the nose I will use them only against thin skinned gv's with very good results. The rate of fire is right on par with the US .50 cal as well, regardless if the 13mm is mounted in wings or cowling (various sources put both the US aircraft version of the M2 and the German MG131 @ 800 to 900 rpm).
It is like comparing getting hit by Mike Tyson or Evander Holyfield.
The other thing we don't know exactly is how HTC has the damage modeled. Those of us who have been around and studied firearms, military weapons theories, etc, are all too familiar with the 5.56 NATO vs 7.62 NATO vs 7.62x39 Soviet vs 6.8 SPC, etc, and the debates of "which is better/best". No matter how it is looked at the wee little 5.56 NATO produces the most violent and horrific wound channels, yet appears to lag behind in penetration capabilities especially at extended ranges. The 7.62 NATO is the "best" in terms of long range penetration and down range accuracy, but the wound channels are much "cleaner" at any range. A single US .50 cal may do more damage to a house per round, but vs an aircraft there may be more "transfer" from the German 13mm to the aircraft than the US .50 cal. It is hard telling. I tend to group the weapons in to the same category and keep that mindset when using them (.30 cals; .50 cals; 20mm's; 30-50mm's; etc).
In short, do not discount the German 13mm. It can and does get the job done just fine.