Kodak let you store more pictures on the same space thru the use of
a higher compression rate for the JPEG - more data is lost to the
lossy compression of the raw picture data to the JPEG format.

And, unfortunately: yes, your pictures will not print "as well" if
you by that mean that it will not look good at high magnifications -
beyond 20-25cm on the "long side" - as your cousins pictures, should
you compare them side-by-side.

The D580, like most Olympus cameras, offers two settings, SHQ and HQ, that
are at the same resolution.  That is not to say that they are the same
quality.  The settings differ in the amount of compression of the JPEQ file.
Theoretically, less compression should give a better image.  However, with
my two Olympus cameras, I have never seen any noticeable difference between
the two settings printing up to 8 X10 inches.  Therefore I generally use the
HQ setting.  It is better to compress more, rather than use a lower
resolution.

Kodak, unfortunately, does not offer any choice in their compression.  The
highest quality setting on the DX6490, I believe, compresses the file even
more so than the HQ setting on the Olympus.  That is why the file is so
small for a 4 MP camera.  Never having compared these cameras, I cannot say
whether this will really make any practical difference.  However, I do know
from experience that a large zoom, such as on the DX6490 can sometimes make
the difference between getting at least a good picture...and no picture at
all.

What they said... and bear in mind file size is *also* dependant on the
image content, when you are talking about compressed files (eg JPGs).

Images with large amounts of detail, or with large amounts of grain,
will not compress as much as those without.