I used mencoder to convert a file that was 720x480 to 1024x740. Then I converted the same file to 1280x740. You would expect the video to look different due to the different aspect ratio, but it looks the same. Why is that?
Perhaps the encoder stored the resulting pixel aspect ratio, and the player honored it.
NTSC DVD uses 720x480 for both 4:3 and 16:9. The difference is the pixel aspect ratio: the former is taller/skinnier and the latter is shorter/fatter. Unlike your monitor, the pixels are not square. If a naive player displays the video pixel-for-pixel the video will be distorted in both cases, since 720x480 is actually 3:2. To be seen correctly, players need to take those encoded pixels and stretch them, using the pixel aspect ratio. For example, 16:9 might be displayed as 854x480.
When you have a frame's worth of pixels, you can resize that frame into any dimensions you want. For example, if the video is low quality, you might save space by reducing the number of pixels across by half. But you don't want the picture to be half as wide, so you double the width of the pixel aspect ratio to compensate.
An encoder might allow you to specify any frame dimensions, and then "help you" by doing the fix-up automatically. There might be other options to turn that off or override it.
But more generally, there's usually no point in resizing video to make it larger -- players are usually capable of doing that automatically. Unless you're also doing some other processing at the same time, like detelecine or decombing, all you end up with is a larger file that doesn't actually look any better. And you would have to watch it at exactly that size, otherwise you are enlarging it twice, which will make it look worse. Better to keep each pixel as-is, perhaps with some cropping.
Also, why those two sizes -- they don't seem standard? And at what "same" size did it actually get displayed?