In law, a postcard is any single sheet of thick paper or card, of any shape or size, with the correct postage stamped on it, and the word "postcard" clearly written or printed on it. If a newspaper, or other competition holder, attempts to restrict their definition of "postcard" by arbitrary category of shape or size, then they are in the wrong (although probably your only practical means of protest is not to enter their competitions, which might defeat the object of the exercise).
Most competitions that require postcard entry usually acknowledge this state of affairs by specifying that a sealed envelope may be substituted in the place of a true postcard.
As to what postcard you should use, I make my own, hand-drawn, and usually A4 in size, although I have gone up to A3, notably for a Telegraph competition for tickets to see the Spice Girls at the 02 (the illustration in question was Geri Halliwell bathing in a giant mug of gingerbread latte by a well-known coffee shop chain).
I generally try to produce an illustration appropriate to the subject of the competition, & have enjoyed a reasonable rate of success, and the Telegraph Motoring supplement briefly loaded a selection of the 20+ plus postcards I sent them on their online gallery section.
Of course, an A4 postcard has four times the surface area of an A5 picture postcard, & eight times the area of a conventional A6 postcard, so it, technically, has a proportionately greater chance of being randomly drawn, but I was always told, the English only invented fair play because, if you don't have it, you can't cheat, &, anyway, it's not cheating unless it says so in the rules.