I'm new to photography and am looking for a solid not-too-expensive mirrorless camera. Through a recommendation by noenken on a thread I've been looking at the Fujifilm X-E1, as it is cheap and quite good from what I've saw. However, the Olympus OM-D E-10 II looks very nice as well. But, I do not know a lot about cameras so I'd appreciate if someone who is more knowledgeable than me could explain the advantages of either one (due to the Olympus being quite a bit more expensive I expect that it has the upper hand in some things, but I'm not sure).
Also, I've been hearing that the Fujifilm X-E1 doesn't have a very good EVF and that the X-E2 has a better and improved EVF and with better autofocus (apparently the X-E1's autofocus is very jittery). Has anyone has any experience of this? Or any advice?
The X-E1 is cheap. Those go for 150,- Euro used here in Germany. That is why it is a good first camera. The autofocus is slow, the EVF looks old by today's standards and video ... just don't. But you can still do a lot of things with it. And as you said, you are new to photography. To have a camera that does just the basics is the best thing to learn what is really important.
The OM-D should have better autofocus system, Olympus is pretty good at that. Video will be doable with it as well but to make enjoyable videos takes a lot more than just a camera.
The downsides of the Olympus are mainly the price and the sensor size. The Fuji has an APS-C sensor, the Olympus uses a micro 4/3. Also the APS-C is in a standard 3:2 aspect ratio while the Oly sensor is 4:3. So you get a more square image on the Olympus and a more wide or high image on the Fuji.
But honestly, don't overthink your first camera so much. It is probably the wrong one anyway. But you won't know until you pick one.
Here is a bit of general advice:
Don't buy into dead or weird systems. Nikon F, Canon EF, Panasonic and Olympus micro 4/3, Sony E, Fuji X... those are affordable long term mounts by reputable brands. Samsung just scrapped their camera business, Nikon 1 and Canon M are not doing incredibly well, Pentax is a bit odd at the moment I think... Play it safe.
Put as little money in the first camera as possible and spend more on the first lens. Every camera will be old tomorrow. The lens will still be the same quality of glass in ten years. Buy both things used, you might end up switching to a different system when you know your needs a little better.
Do some training! Look for courses at photo stores like Adorama, Calumet, B&H, I don't know what is around you. Most of them have beginner stuff for cheap, sometimes for free. Learn the basics, aperture, shutter, ISO. From there on everything else will be manageable.