Could it be the finish on the particular handle that you dislike as opposed to the stabilization? I find that stabilized wood still has the same feel as nonstabilized wood (still has the same grain, but doesnt shrink and swell as much). However, if you coat a piece of wood with boiled linseed oil or tru oil, it might cover the wood grain and feel "plastic-y". Or if the wood is sanded to a very high grit to bring out the look of the wood, that can feel very smooth compared to say a rough sand on ho wood. Maybe try knocking down the finish on your handle with some 220 grit sandpaper and see if that changes things.
I agree with this in general. Stabilized wood tends to be similar density to heavier woods like ironwood or blackwoods. The actual density depends on the specific wood though. So that's definitely something to consider.