I am not sure what "automatic" mode you selected on the Olympus. However, based on your jpegs and metadata, we can report a few problems and then I may suggest solutions to fix them :
- The Olympus went for maximum shutter speed (1/2000) and a small aperture (f/8) at high ISO (1600). We could endlessly about why the camera achieved these settings in an Auto mode. We would never know. In the end, those settings applied to landscape photography results in poorer detail resolution due to poor sensor exposure leading to excessive ISO noise.
- The Olympus metered a bit overexposed. In harsh sunlight, the dynamic range is so wide the camera couldn't capture it altogether. It have preferred to keep better shadows by blowing the snow and sky at the horizon.
- Due to facing sunlight, the camera focus acquisition may have messed up due to the flares in the lens. This could explain the small excess of blur other than ISO noise increase.
- We could continue forever on the poor camera choices in this situation...
Despite all the approximations the Olympus camera did, the resulting photo is not "pure garbage". You obviously had higher expectations, especially looking back to the Gopro shot. Here is how to ensure maximum image quality for landscape photography :
- Use a small aperture to have a large depth of field that covers most, if not all, of your subject.
- Make sure the camera is using its base ISO (100 for your camera).
- Double check focus accuracy by using 100% crop live view. Adjust focus manually if needed. Unfortunately, the Olympus Stylus 1 does not have focus peaking to assist you in this task. If using a tripod, disable stabilization.
- check exposure histogram and adjust exposure compensation accordingly. You may need to use a ND filter in very luminous situation like this. Otherwise the camera might not be able to apply the calculated shutter speed (above 1/2000 for your camera).
Bottom line :
Despite the Gopro having a better handling of this particular situation, a camera is just a tool. In auto modes, it won't make the right choices everytime. It will work OK most of the time. However, in special case like this (harsh sunlight landscape with front facing sun), the results are typically worst than expected because the camera doesn't have a clue of what it is photographing. You might want to learn how to operate your camera in A, S, M mode to be sure it is taking the photo you want. You may also learn about ETTR and raw processing for optimal image output.
Brand related opinion :
I found that Gopro have a great auto mode that suits most traveling situations. It also has appealing default color and settings. It is all about capturing any moment without worrying of the technical side. However, I found it lacking for photography in terms of Image Quality and settings/capabilities. But who cares on Instagram or small prints. For me, Olympus philosophy is in the opposite direction. While it offers lots of customization and handy tools, they are buried under a not so indicative menu system. Plus, the default settings and color science is certainly not the most appealing. To get pleasing JPEGS out of an Olympus, you must learn its capabilities and tweak it to your convenience. You might learn some things about your camera via this extensive review and its samples.