my experience with bounce has been only near large obelisk type land formations, or deep in valleys next to flat surfaces. it's a condition of multiple reflective signals with the same time stamp, and the GPS not sure how to handle the variations in them.
in heavy tree cover, while moving, i have not seen bounce. i would imagine (speculation) that there are large rocks/similar that are giving repeated ping reflections , and causing the bounce.
what you've discovered is that BOTH stand alone and smartphones suffer from bounce exactly the same, when it's caused by land formations.
look at the devices, neither of the hand held GPS devices you mentioned have a two meter antenna sticking up through the canopy, so when you see similar results, you're basically verifying what testing has shown:
there is no difference in accuracy between modern devices, stand alone or smartphone.
the really bad thing to realize is that the cache placer also likely saw that kind of bounce! did they average, or just toss the cache and record the cords after half a minutes effort? you'll never know.
what you can do to verify your location matches the caches listed cords(correct or not) is to use waypoint averaging. your stand alone should have a function for averaging, and i know your smartphone does. you can average two or three times, if you like, to make sure you had be reliable cords, and then move in the direction you think you need to, average again, repeat. this has gotten me to within a cache that was more than forty feet off, on more than one occasion. making a note about bad cords didn't have a result, so i gave up on the process.
you can end up within 4-5 feet, or less, depending on land masses, with averaging. give it a try. :-)
The first cache was under the canopy near large rock formations. The hider mentions in the cache description that they averaged the coordinates over 600 times and that there would be problems with GPS signal. The second one had no large formations, but was in the middle of a densely packed wooded area and the hider made no mention of averaging. I had similar results with both caches, constantly being moved over a 60 foot radius. I'm not expecting 4-5 foot but when you're looking for a micro in the woods it would be nice to get within 15 feet. I'll try averaging, thanks for the tip.