Allow me to add two cents here - keep in mind that I am not talking with a "X engine is better than Y" mindset, just sharing my experience.
That is not true. Sure thing, 90% (or more) of the content is fighter oriented, but there are other type of games done in Mugen, like Shoot em up (ironically, the engine started as a shoot em up engine), exploration, Pokemon-like duels and etc. Even Beat em up were made with it.
This is not exactly true. Depends too much on the coder behaviour. Keep in mind that Mugen was thought, since the start, to be a modular engine - so every content should work against any other content - an "open enviroment" , while OpenBOR works on a more "close enviroment" most of time - in other words, things in OpenBOR workes where they are made to. In Mugen terms, we call this "a closed game".
When working on Closed Games, things works differently and you can reuse assets on a very efficient way.
STRONG POINTS
OpenBOR
Portability - there are several ports for the engine (official and unofficial), so you can have your game running on more platforms
Active development - The engine still has a development team, so possible bugs and improvements can be added to the engine.
Open source - Anyone can contribute to the development of the engine.
Ease of development of Beat em ups - Platforms, holes, items, are much simpler to do in OpenBOR
Practicality in some animations - Want an animation of your character holding the other? Just create an animation called "GRAB" and that's it, just approach the target.
MUGEN
Content - With over 20 years of existence, it's incredibly easy to find content for Mugen (and the creators have always contributed a lot to the sprite rip process). Pretty much everything has been made for Mugen, from Ryu to Ronald McDonald.
Community - There are still several Mugen communities, and finding help is very easy.
Accurate Log/Bug Report - In Mugen, when there is an error, the engine reports exactly what is happening and where the error is. For the engine to "simply close", some file needs to be severely corrupted.
Front end / Editor - Mugen has several frontends for content development, with some extremely complete and easy to use, such as
Fighter Factory.
Sprite Scaling - Allows you to rotate or scale content smoothly, without jagged edges and even allows for native interpolation.
Backward compatibility - It works perfectly, the developer just needs to put it in the code for which build it was developed and, from that build onwards, the content continues to work.
WEAK POINTS
OpenBOR
Editor - A unique and stable editor is missing for content development. Although there are some editors, all of them either don't support everything OpenBOR has or are unstable and buggy, unfortunately even corrupting files sometimes.
Log/Bug report - It is incomplete and does not bring all the information. For a long time, you didn't even know which build you were using. There are simple errors that simply make the engine crash in your face without saying what is causing the error.
Documentation - There are still undocumented things in the engine (and not for lack of effort from people to help with that), but because some things were added to the source code without any documentation and only the original programmer knew what it was actually for .
Lack of basic concepts - Certain mechanics are missing from OpenBOR, and if the creator wants some of them, he will have to program them from scratch. An example is friction with the ground: there is only the physics of gravity, but not ground resistance. The same goes for your character not "passing through" the enemy - there is no collision between bodies, your character passes through the enemy if he walks by him.
(I know this was on the update list, but it's not available to use yet)
Backward Compatibility - Doesn't work at all, with some points preventing engine progress in some cases. In other cases, compatibility has been broken and some content no longer works, which makes the user have to use (and know) exactly the build that was used in development
MUGEN
Inactive development team - The responsible company seems to have abandoned the project (the last update was in 2014). However, today there is a "spiritual successor" called IKEMEN that, for the first time, managed to have an engine compatible with everything that Mugen offered and expanding even more. This engine is still under active development
Portability - Mugen only officially runs on Windows. The linux version is extremely old and there is no official port for Android.
Interactivity with scenery - It's something that Elecbyte, developer of mugen, was asked to exhaustion, but it was never answered. We only have a few codes and, to achieve this, we must resort to workarounds.
Closed Source - There is no source code of the engine.
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Both are very capable engines, but have their own specific uses. As I usually say,
using OpenBOR to make a fighting game or Mugen for a beat em up is like eating soup with a fork: it's possible, but there are more appropriate tools.