What are the sequence settings of the high resolution sequence(pixel dimensions)?
Sequence pixel dimensions will help others understand what you are doing.
It is most likely HDV but your post doesn't give that info.
16x9 isn't real helpful as that could refer to HD or SD footage.
Try exporting a Quicktime (reference or self-contained- NOT Quicktime conververison) of your high res seq.
See if everything looks correct in QT (size, color correction, etc.)
If it does:
In FC drag your 16x9 hi res sequence into the 4x3 sequence and then scale from there.
If your 4x3 version is for DVD you should make sure everything is 4x3 title safe.
If it will only play on a computer/web you don't need to worry about title safe.
If title safe is an issue:
duplicate the16x9 seq
remove the GFX
drag 16x9 seq(sans GFX) to the 4x3 seq and then add the GFX to the 4x3 after you scale the video.
If your hi res seq is HD and your make it SD. It will not look as good. 4x3 is normally an SD delivery option. HD will always look better than SD.
For higher quality scaling than fcp, export the original sequence as darbypsnm suggests, but bring this file into compressor and use the geometry panel to crop the image to 4:3 standard def and set the resize filter in the frame controls panel to "best." If you need some help with compressor, post back.