It depends on what type of images you're dealing with. If you're dealing with photographic images, JPEGs will almost always be smaller than PNGs, with no discernable loss of detail as can be seen by the human eye.
Conversely, if you're dealing with highly non-photographic images such as GUI elements or images with large blocks of solid colors, then PNGs and JPEGs will be comparable in size, but the PNG will save losslessly whereas the JPEG will be lossy and have very visible artifacts. If you have a really simple image (very large blocks of constant colors, e.g.), then a PNG will very likely be much smaller than a JPEG, and again will not have any compression artifacts.
The act of saving an image as a PNG or JPEG should not take up very much transient memory. When an image is in memory, it is typically stored uncompressed in memory so that it can be drawn to the screen very quickly, as opposed to having to decompress it every time you want to render it. Compared to the size of the uncompressed image, the amount of extra temporary storage you need to compress it is very small. If you can fit the uncompressed image in memory, you don't have to worry about the memory used while compressing it.
And of course, once you write the image to the file system in non-volatile storage and free the in-memory image, it really doesn't matter how big the compressed image is, because it doesn't take up main memory any more. The size of the compressed image only affects how much flash storage it's using, which can be an issue, but it does not affect high likely your app is to run out of memory.