Both fine cameras. The differences will mostly come down to particular features, how they both handle in your hand, and price - you won't go wrong with either one, so figure out if either camera has some particular feature you really want or need that the other doesn't...that can help you decide. Or whether one feels comfortable in hand and the other not so much.
You asked about the LCD display on the Sony - it does actually have the ability to face forward for self-portrait work - it tilts down 180 degrees (under the camera), and can then swivel 180 degrees to face front or back. If you were hand-holding the camera to take photos of yourself, no problem with either camera. The only downside to the Sony design is if you intended to take a self-portrait with the camera on a tripod, as the LCD screen is pointing towards you from under the camera, which would be partially blocked by the tripod head...though tilting the camera to portrait position on the tipod could make a bit more of the screen visible.
Remember too that there is a difference between the two cameras when used in 'live view' mode, which is when you are looking at the LCD screen. The Canon is a traditional DSLR, so it is designed to be used with an optical viewfinder and traditional mirror - when you switch to 'live view' to view the scene on the LCD panel, the camera has to flip up the mirror inside (which is providing the view for the optical viewfinder and also to the autofocus sensors off a secondary mirror), and use the main sensor to feed the view. When doing this, it can no longer use its focus sensors without flipping the mirror back down, focusing, and flipping it back up again....or it has to use contrast-detection focus off the main sensor, which is much slower especially in low light. Both processes mean the time to focus, and the time between pressing the shutter and getting the shot, can get quite long, with a big delay waiting for the camera to go through the process - sometimes a few seconds or more. The Sony on the other hand is a hybrid design, using a partially transparent fixed mirror. Rather than an optical viewfinder, it uses an electronic one, so it is essentially functioning in 'live view' mode all the time, whether you look through the viewfinder or the LCD. What this means is that the mirror is only feeding data to the autofocus sensors, and doesn't need to flip back and forth, since it's partially transparent. So when switching to the LCD view, the camera doesn't change anything - the view remains live, the focus remains in full phase-detect mode, and no mirror assemblies have to move to fire the shutter. Which means no delay, no loss of focus speed, no mirror movements to refocus - the camera works identically whether working off the viewfinder or the LCD.
This also pays dividends when shooting video with the camera - DSLRs are often touted as being used to film TV shows and movies, and indeed they are - of course, they're attached to full rig systems, focus pullers, external video monitors, etc. costing many times more than the camera...and they're being used by professional cinematographers. The typical consumer who wants to shoot some video of their child often expects a 'camcorder' like experience - press record, follow the subject, and the camera handles exposure and focus. Unfortunately, for the same reasons as the live view mentioned above, DSLRs have that mirror assembly moved out of the way, cutting off the focus sensors, in order to show you a live view (and to shoot video). Which means, you either cannot autofocus at all, or you have a very slow and unreliable contrast-detection based focus working through lenses not designed for that use. The Sony design specifically addresses autofocus during video, as the fixed partially transparent mirror allows full-time phase detect autofocus even while shooting video - meaning superfast, accurate, and reliable focus even in very low light. Professionals who want more specific frame-rate control, aperture control, or slave control may prefer the higher end full frame DSLRs even though they cannot autofocus because they'll be using them in rigs that can focus the camera, and gives them more manual control over the shoot - but for the average consumer, fast autofocus during video is often much more useful, and much more what they might have been expecting just like the old camcorders of the 90s.
Hope that helps explain them a bit!
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses