The NEX cameras have the same size sensor as a majority of DSLR cameras - APS-C sized. This makes the camera capable of image quality that you could typically only get from a DSLR...especially shooting in low light situations. This is the primary benefit over any P&S camera - it will perform substantially better than any P&S model in almost all situations. It is also more advanced than most P&S models as far as the abilities. It will not compare to a DSLR overall, as the interface is more simplified, controls typically available with exterior buttons on DSLRs for advanced manual control of the camera are hidden on the NEX within the menu, and without an optical viewfinder, performance in areas like tracking moving wildlife or quick moving action sports will be difficult. The controls are mostly still there - they just take more menu-diving to get to. This shouldn't affect typical to advanced amateur shooters, or folks who don't emphasize sports or wildlife photography.
I would encourage you to handle the two cameras, and try out the menu controls in person to see how the camera 'fits' you - you may find the wider and flatter NEX3 grip better, or the more extended, rounded NEX5 grip better...or you may not like handling either one. Ergonomics are important, so don't let others tell you that the camera is going to be great or horrible for you - only you will know once you've handled them.
The LCD is excellent resolution, and is tiltable at angles - shooting will be P&S style using the LCD as there is no viewfinder (an optional electronic viewfinder will be available in the future)...those used to DSLRs and wanting an eyepiece may have trouble with this, those coming from P&S cameras should have no problem at all.
The camera will shoot excellent quality up to ISO6400 - way beyond a P&S camera...and has additional tricks for even better results like the in-camera 6-frame stacked twilight mode for extreme clarity in low light, and the 3-frame in camera HDR mode for capturing extreme contrast dynamic range situations.
The menus include extensive help descriptions and walk throughs for beginners...these help screens can be turned off (some descriptions remain) later once you get the hang of it, or left on if they help you. The camera will function in complete automation in iAuto mode - you will have no input at all over what the camera does - it does all the work. Switching to P mode will function much the same - fully automatic...but will allow you to override the camera's decisions in a few key areas, like EV, ISO, and white balance, if you desire. Then, switching to A or S mode lets you begin to control some of the parameters of the exposure - either the Aperture or Shutter speeed. And there is a full manual control for when you're confident with what you are doing. Similar to a P&S, there are Scene modes which have certain default settings saved for specific styles of shooting.
As for NEX3 vs 5...they are not drastically different other than video, LCD screen resolution, and design/build. The NEX5 is significantly better built - actually as good as any top-line DSLR with a magnesium alloy chassis and metal build. The NEX3 strips down to a more basic metal body and chassis with plastic trim, to save money, and a lower res LCD screen. Image-quality-wise, there's probably not a big difference between them.
Good luck in deciding - they really look like neat little cameras with some great abilities, much better than P&S models in abilities, but no replacement for a DSLR. If you're looking for something in between or smaller than a DSLR, they should fit you very well...just make sure you're comfortable holding them and working the menus, and enjoY!