The Galaxy buds do not have on board storage. I never really understood on board storage on buds anyway. First all my music is through Google Play Music so Samsung won't let me transfer that, second how do you even control and pick songs. It is not often that I have a need to listen to music and my phone isn't also on my person. If onboard storage is a deal breaker though you definitely will want the iconx
I thought I heard the buds have 8 gb of on board storage, but I couldn't find that anywhere on the internet. Just going through the Galaxy Wear app, you're right, there is no way to add music.
So, let me explain on board storage. It allows you to leave your phone at home if you want to go for a run or walk around the neighborhood. Plus it cuts down on battery expenditure on the buds. Playing music from the buds' storage doesn't run the battery down like it does when you stream from your phone. The original iconX had this option.
Personally, I wouldn't buy the original buds at this time. You probably won't find an unused set to begin with. Even if you did, they'd probably be near the same price as the new Galaxy Buds. My original iconX batteries barely last an hour. Sadly I have no experience with the ixonX 2018 buds, but what I've seen online, they're about $40 more expensive than the new Galaxy Buds.