Copying timeline to new sequence lowers resolution
It appears that your pixel aspect ratio and interlace/progressive choices differ between the two sequences.  What you are seeing is a combination of the interlacing and the change in pixel aspect ratio (which results in the image having to be scaled to a new set of pixels that aren't exactly like the original.

For playback on a TV that supports interlaced video, you won't notice a whole lot of difference, but on a computer or progressive display, it will look funny.  For best quality, you will want to use a progressive, square pixel sequence if you are outputting to PC or to a progressive display (such as 1080P or 720P TV).

The bad news is that it doesn't appear there is a good way to make any changes to the sequence that you need to make while there is content in it, but if you make a new sequence, you can go to the settings tab and specify everything the way that you need them specified.