Your friends think that the "big ones" are "dslr 35mm like a Nikon or Canon" and you trust them?
First, the big ones aren't the Nikon or Canon dslrs, they're the medium and large format cameras which are much bigger and do some things much better than the dslrs. Still, the dslrs do some things better than the big ones. Try doing sports photography with one of the big ones and you'll quickly downsize to a dslr. Try doing landscape photography and provided you don't have to carry the big view camera and tripod on your back to the top of a mountain, you will choose the view camera over the dslr when it comes to image quality.
Second, Nikon and Canon don't make any "35mm dslrs". No one does. 35mm is a film size and dslrs don't use film. What Nikon and Canon, and a few other manufacturers, make are slrs with a sensor the same size as a 35mm negative. They're called "full frame", not 35mm, because full frame refers to the image capture size and 35m refers to a film stock size.
So, if your friends don't know what the "big ones" are, or that there's no such thing as a "35mm dslr", why would you trust them to know about anything else?
There are a few reviews around including this one:
Full review: The Olympus OM-D E-M5
which compare the Olympus OM-D E-M5 favourably to Nikon D700 and D800 full frame dslrs. Ming Thein, the author of this review, comments at one point in this review "Frankly, in good light, with a contrasty subject, it gives my D800E a run for its money." He has professional experience with Nikon and Leica full frame digital cameras and also uses an E-M5 for professional work. That's a pretty good recommendation for a micro four thirds camera. There are a few professional photographers on this forum also using micro four thirds cameras professionally.
Yes, there are some things that a micro four thirds camera won't do as well as a full frame digital camera, the two main ones being providing very shallow depth of field and providing good continuous auto-focus for action shooting. You can get quite shallow depth of field with micro four thirds with the right lenses and you can do action shooting with it also, but you have to work harder to get good results and you won't get as high a proportion of good results. For pretty much anything else you will have no problems with micro four thirds and you can turn out extremely high quality results.
So read a few reviews, take a look at the photo threads here and the photos in the reviews, see what people say about the cameras in the camera discussion threads here and make up your own mind, but don't forget that your friends don't know what they're talking about if they think Nikon and Canon are the "big ones" and that they make "35mm dslrs". Both of those statements are inaccurate information.