BBX is wireless - bluetooth compresses the sound, in comparison to pistons - BBX will sound a bit veiled and narrow
Have no idea about stock HTC One, this is Note 2 accessories section so we all got N2s
If yours came with HTC Beats, they might be ok, but in general Beats make their bass bloated and with recessed mids.
Comply will work with anything, probably T400 or T500 since tip is wide. Personally, they work better with sony hybrid tips (a lot of ebay "hybrid" tips out there. i ordered one for $0.99, will update pistons review once I get it).
There are a lot of other great choices, but more expensive. If you like bass and nice balanced sound with great vocal clarity, I'm in a process of reviewing Beyerdynamic new line of IEMs. MMX 102ie has in line remote but no volume, while DX 160ie without remote but slightly better bass. Both have amazing clarity and dynamic sound. Each one around $100. Both of the reviews should be up later tonight if I finish it. I post all my reviews in General Accessories section of XDA where my Index page (link in the sig) is a sticky. Subscribe to it or visit that section not to miss all the reviews!