Powershot A20 has a very short lens: f/2.8 – 4.8; 5.4mm (Wide angle) – 16.2mm (Telephoto); focusing range: Normal: 76cm (2.5 ft.) – infinity. It has a very short focal length and thus, the hyper-focal distance is quite close to the camera. Everything is in focus. A dSLR with APS-C sensor like your 60D has a much larger sensor, and much longer lenses (typically). For my APS-C bodies, I have a 10-20 mm lens. At 10 mm, the field of view is 90 degrees. Much wider than the field of view you get from the A20. The long end of the A20’s lens is still shorter than the short end of the kit lenses that come with APS-C bodies. As focal lengths get longer, the hyper-focal distance moves further from the camera, and depth of field shrinks if your subject is closer than the hyper-focal distance. This is a very brief discussion, but there is a lot about depth of field and hyper-focal distance on the Internet. Some information is better, some worse, but lots available. Full frame bodies have even bigger sensors, so at the same focal length you can get even closer to your subject so there is even less depth of field for the same framing.
With respect to http://www.flickr.com/photos/areallifegirl/11427614883/, the groom’s right shoulder is partly out of the frame. What would have happened if you moved a step or two, maybe three, to your left?
Those flowers look slightly burned out in the centre? Are you shooting to raw files? If so, you should be able to recover that detail. If not, look up Highlight Priority in your camera manual. You get much more latitude out of raw files but if there is some reason to avoid raw files, Highlight Priority will help. The photo would have been helped by some fill flash. They are squinting and light is not getting into their eye sockets. As in the other photo, her shoulder and arm seem to be brighter than their faces. Their faces should be slightly brighter than the rest.