There are lots of opinions on the TONE you get from different nuts due to design and material it is made of...
However, tuning stability has only to do with two things - are the openings for the strings wide enough and are they smooth to allow the strings to slide when manipulated. You could buy a new nut, but unless you are looking for better tone it is very easy to fix your nut. This means no cutting out yours, chancing cracking the finish if you dont exacto knife perfectly and eliminating the new nut not lining up/being imperfect etc....
I have an SE singlecut and an SE C24... I did the following to both nuts and have had zero problems with tuning stability (although, to be fair, they both got the John Mann locking tuner upgrade - BIG SHOUT OUT to John Mann - the conversion is awesome!!!!!).
Take the guage string you want to use and put a peice of 800 grit sand paper bent over the end of the string (if youre replacing strings, use the old ones so you dont have to worry about kinking them). Run it back and forth in the groove a few times. Focus on widening the groove, not deepening it (ie more pressure on the sides). Once that string slides freely, wrap some 8000 grit sand paper over the string and then repeat the process. This time push on the sides and the bottom of the groove, as you arent removing material with this small grit paper, but instead burnishing the nut to make it very smooth. Quick vacuum to get rid of the dust and restring. You’re ready to rock.
I play my SE C24 aleast 3-4 times a week for an hour or two and haven’t had to retune for months at a time once the strings are broken in....
Check out this link from Phillip McKnight that taught me how to do this. It also has tips on replacing the nut if you chose to go this way.
You can also order liquid graphite to put in the nut slots, but have never needed it once the above was done.
