Hey folks thanks for the replies. I am upgrading from a point and shoot, yes. I will primarily use it for taking day to day pictures, but I want something that will give me great professional shots. From doing all of the reading, it seems to me that the Sony is nice and compact and easy to carry around, whilst the Canon is a bit bulky. But looking at the images, it seems that the quality of pics from the Sony is not as good as that of the Canon.
The image quality potential from both of these cameras should be quite on par - there's no reason either one should be significantly better than the other. It's hard to base the decision on looking at sample photos from people, as it has more to do with the skill level of the shooter and the lenses used - if you looked at 10 sample photographers from each camera, and 8 of them were experienced on one camera, and 8 were complete amateurs on the other, it would make the latter seem worse. Truth is they both have the same size sensor and the same image quality potential. They're very different cameras in style, design, and each has strengths and weaknesses - it's more important to decide which would work best for your needs.
A DSLR tends to be much bigger, heavier, bulkier. A mirrorless APS-C camera like the NEX will tend to be slower to track focus on a moving target, have a more limited lens selection, and has no optical viewfinder. Smaller body usually means smaller buffer (how many continuous shots you can take before the camera slows down) and smaller battery life. But it also means more portable, lighter, smaller lenses, electronic viewfinder (which has some advantages over an optical one, and some disadvantages).
If you're primarily coming from P&S cameras, then optical viewfinders are likely not going to be a need or an issue - you've never had one before, so it may not be necessary. If you're going to be shooting primarily scenics, landscapes, portraits, snapshots, etc, then focus tracking ability, buffer size, and burst speed likely aren't going to be key issues - a mirrorless can yield just as good results as a DSLR. If you intend to shoot moving targets, sports, birds in flight, or other subjects that require continuous tracking focus and panning skill, a DSLR will be a much better tool.
I've been shooting with both a DSLR and a NEX mirrorless camera side-by-side for over a year - I can verify 100% that there is no discernible quality difference between the two...if I posted two shots, one from each camera, you would not be able to tell which was which. The sensor size is identical, the resolution is identical, the depth of field is identical, and the rest is up to me as a photographer getting the exposure, color, and focus correct. As long as I'm using equally good lenses on either camera, there's absolutely no quality difference. But I know there are times when the mirrorless camera's advantages of portability, size, and discretion are highly desirable, and other times when I need the larger DSLR's tracking focus, big buffer, and big battery life, as well as the heftier grip and weight to counter-balance big long lenses.
I'd guess that the mirrorless camera will probably suit your needs easily enough, can deliver pro-quality results if you decide to invest the time to learn more about photography and get more lenses for it for each situation, and will be lighter, smaller, and more convenient overall. I'd recommend considering the DSLR route only if you think you'll need the faster tracking focus or the bigger body for ergonomics, or intend to really get deep into the hobby and want very specialized lenses that may only be available in the larger lens collection of the DSLR mount.
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