There is a third option for you - as others have suggested, you can use a tool like Handbrake to extract the content from your DVDs, but from there, if you’re feeling adventurous, you can acquire a higher quality release from… Somewhere else… Get it in .mkv format, and you can use a tool like MKVToolNix to extract the audio from your DVD copy and “mux” it onto your HD copy.
MKV files are great because they are really just containers (like a fancy .zip), keeping the audio and video independent, allowing you to easily swap one out for the other.
The only downside is you may have to edit the audio slightly to sync up with your video