Any version of Money should open Money files that are from that version of older. So, if you have Money 2003 installed, it should open that version and any earlier version file. If you have a Money 2004 file and try to open it with Money 2003, you'll get the exact error you've mentioned.

Also, note the one exception is international versions. In general, most versions of Money will only open the same country's files, i.e., a file created in US Money will not open in UK Money.