Should I give up on FM HD over the air ? and steam instead ?

Better by you better by me.

Only you can determine if it is. Try it.

My local FM HD is inferior to the same signal via FM. I have the excellent Sony XDR-F1HD (modded) to hear HD. I also have 3 slightly better tuners that are FM only.

Modifications, Upgrades, Repairs (xdrguy.com) 

Just a guess but over the air probably sounds better. 

HD radio uses lossy compression, so a good over-the-air signal often sounds better.

If the OP lives 10 miles from Manhattan, he probably doesn’t need a powered antenna to receive WBGO from there. In fact, he may be able to get a quieter signal with just a simple dipole, and it's possible that WBGO's analog signal will sound better than the station's HD signal or its stream.

Stream everything its great.

Yes

If you have a decent tuner and adequate antenna, over-the-air is better.  I tried Sangean and Day-Sequerra HD tuners; neither came close to decent FM.  I hear that the McIntosh HD tuner sounds good but is scarce and expensive.

You must be really mad about it if you want to steam.