Just to add some information:
35mm photos rely on lots of factors, mainly :
the camera shooting the image
the conditions of the shot
the paper printed on
the machine or person processing the picture
the color correction process used in printing
the chemicals used in processing
But to give an average widely accepted would be an equivalent to about 11 Megapixels
Digital cameras also rely on a lot of factors, mainly:
the camera shooting the image
the conditions of the shot
the paper printed on
the machine AND person processing the picture
the color correction process used in the printing
the color correction process used in the camera taking the shots
the color correction process used in the photo capture/editor
the compression algorithms used in the camera
the compression algorithms used in the photo capture/editor
Just to name a few. As you can tell, there are lots of factors involved in good pictures as well as many others. As an avid user of both means, your images are only as good as your media of presentation. In other words, if you take a 6000X4000 pixel image, it wont matter much if you compress the image to the point that grain is completely evident as well as compression jaggies, and then print it out on a 6 year old hp color printer.
All things being semi equal, a 2-3MP camera printing 5X7 shots as mentioned above will produce satisfactory prints from a fairly modern color printer on very good photo printing paper. Paper makes a huge difference.
The type of printer also matters. Inkjet printers can only reach a certain amount of dots per inch but that is only half the story. If the paper you print to has minute pits and valleys in the paper that let these dots seep through, or sink well below the surface, that color and detail is lost. Also, untrue white background make the image look faded and worn out. Vibrance in color comes from truely bright white surfaces for greater contrast. Dont forget very good black inks help to maintain that contrast.
Printers from stores like Sam's, Wal-Mart, and other grocery stores use printers of the dye-sublimation type. These printers are specifically designed to print images and normally use fairly high resolutions as compared to digital images captured by cameras. Is is not hard to see these kinds of printers able to print up to 300 dots per inch and more. But dots per inch is not a very accurate way to measure these printers. Here is an article from one of my favorite websites, How Stuff Works.com:
"Dye-sublimation printers allow you to print photo-lab-quality pictures at home. As the price of these printers go down, more and more digital-camera owners are choosing to take advantage of this technology. In dye-sublimation printing, colors are not laid down as individual dots, as is done in inkjet printers. Individual dots can be distinguished at a relatively close distance, making digital pictures look less realistic.
If you looked inside a dye-sublimation printer, you would see a long roll of transparent film that resembles sheets of red, blue, yellow, and gray colored cellophane stuck together end to end. Embedded in this film are solid dyes corresponding to the four basic colors used in printing: cyan, magenta, yellow and black. The print head heats up as it passes over the film, causing the dyes to vaporize and permeate the glossy surface of the paper before they return to solid form.
So the main difference between this and other types of printing has to do with heat. The vaporized colors permeate the surface of the paper, creating a gentle gradation at the edges of each pixel, instead of the conspicuous border between dye and paper produced by inkjets. And because the color infuses the paper, it is also less vulnerable to fading and distortion over time."