I believe I see what you're saying.
If I pause a song, there is a very faint white noise sound for ~5 seconds and then the white noise sound cuts off and is dead silent (maybe a battery saving feature).
This is not all that uncommon with Bluetooth gear. It is very faint, and I don't really notice it (probably because I have mild tinnitus).
From what you're describing with the BT3, I would say we are talking about the same thing (ie a faint white noise sound).
However, since your BT10 white noise is much louder compared to the BT3, then I would say something is wrong. Because that faint sound is the same on my BT3 and BT10.
I can confirm both my BT3 and bt10 sound the same as far as white noise goes. Extremely minimal, not noticeable at all. I might hear it between a song playing or call or video for half a second but then it goes away. Definitely, not normal.