I've seen a lot of petty battles over the years where technology is involved. The worst I've seen is Panasonic vs Olympus, driven by the fanatics alone.
My take is that both companies offer something great and without one or the other, the format would wither. This should be Panasonic + Olympus instead of Panasonic vs Olympus.
Panasonic brought about the AG-AF100/AF105, which convinced Zeiss to adapt their cine lenses. Given that the lenses have a typical micro Four-Thirds mount, they work just fine, and I would imagine that you could rent one for your Panasonic GH3. For that matter, you could use it on a Blackmagic Pocket Cinema Camera.
Panasonic has done a lot for video while Olympus has conversely done a minimum for video. However, Olympus is still a leader in still photography, regardless of what Canon or Nikon might have you believe, though they don't have those negative advertisements any longer since their sensors' pixel density is high also.
Olympus is clearly doing a lot with their in-camera processing to provide a great image. When you put a micro Four-Thirds print up against prints from much larger sensors, it's extremely difficult to see a huge difference. Back in 2006, I was printing on 13x19 inch paper with 5.1 MP images from an Olympus E-1, so I can't imagine why a current micro Four-Thirds body with 16.x MP would have a problem competing with the rest. The pixel density should be similar to a 24.x MP APS-C sensor. If the sensor and image engine are the best they can be, it's down to the adjoining circuitry and the analog-to-digital conversion. It's all come a long way since, say 2000, or even 2003 when Four-Thirds equipment was introduced.
If Olympus and Panasonic had not joined forces to develop Live View with the E-330, DMC-L1, and Leica Digilux 3, would there be a micro Four-Thirds now? Would there be a mirror-less market at all?
I suspect that still photography and videography would have been kept to separate devices for simplicity, and profit.
It's not that relatively inexpensive digital motion picture equipment isn't available--RED has proven that--but that students have extremely inexpensive equipment available and can do everything on their own. Panasonic's GH2 and GH3 have shown how inexpensively someone can demonstrate their abilities as directors and photographers.
Live View has affected still photography in positive ways. When you can't get inside the crowd, having that fully-articulated rear display means that you can get the body at an angle and view the scene to get the image you want. N.B. Olympus: Your E-M1 is lacking in this respect (and several others related to the E-5).
micro Four-Thirds is stronger because of Panasonic and Olympus. Take away one company's lenses and you can get by but, unlike Nikon or Canon, you don't have a wide variety of third party lenses, so you need both Panasonic and Olympus selling their system by providing lenses.
If we should believe a Credit Suisse "anal"yst, Olympus and Panasonic will be out of the camera business shortly, along with Pentax and FujiFilm. That will be a dark time and I seriously doubt that Nikon, Canon, or Sony would continue to improve because they won't have anyone to show them how.
Update 2014.03.02: I've had some trouble with my Panasonic 35-100mm f/2.8 lens and I asked Panasonic to repair it. They said that it was fine: http://nobuyukishouldknowbetter.blogspot.com/2014/02/i-wont-be-buying-any-more-panasonic.html
I've been using the Olympus 12-40mm f/2.8 on the GH3 body and it has breathed new life into it. I'm shocked at how much better things look with a proper lens. I'm looking forward to the 40-150mm f/2.8 lens from Olympus later this year. I'm not saying that I'm abandoning Panasonic. I just don't want to use any of their lenses any longer, and I hope that I never have to have anything repaired.
Update 2014.03.15: Since the GH4 has arrived for pre-order, I haven't seen anything to replace the AG-AF100/AF105. The latest product in that category took PL-mount lenses, and the GH4 sales blurb said PL-mount lenses would be useful through a third party adapter. I guess a dedicated micro Four-Thirds camcorder wasn't popular at all, so we'll have to stick with the 29m59s limit of the GH3 and GH4.