Yes, there are differences in approaches between the two companies, even though they often use the same sensor and sometimes create cameras that look similar (e.g. GF-3 and E-PM1).
Panasonic requires lenses to have image stabilization; they do not include it in most of their bodies. Panasonic tends towards more video capability, especially in a few models such as the GH4. Panasonic has the only model with fully swivel LCDs (e.g. GH4). Panasonic JPEG rendering has improved in recent models, but still lags state-of-the-art. In the US, Panasonic has been abysmal at delivering product quickly, and has minimal dealer support.
Olympus uses in-body image stabilization, thus can stabilize any lens. Olympus' video capabilities tend towards automatic and fewer feature choices. Olympus supports off-camera flash in some of their models. Olympus only makes models with a tilt LCD. Olympus JPEGs tend to appeal to users more (more contrast, better color, better noise/sharpening choices).
There really isn't a bad choice between the two, only a lot of small differences. I'm a firm believer that how comfortable you feel with a camera will be a large factor in how good the results you get of it are, thus I strongly encourage you to try both and pick based upon that if there is no single other factor that tilts the choice. The Panasonic GH4 is a larger camera than the Olympus OM-D E-M1, for example, while the Panasonic GM1 is smaller than any previous or current Olympus camera.