Best AV receiver for B&W 703 S2?

What specifically seems underwhelming?

The Marantz SR7015 is a good receiver. I agree with soix that a more detailed explanation of what you think is incorrect or missing is necessary. But to start with if your room is an unfinished basement I would kind of guess everything will sound poor, even a single person singing live.

Well the sound quality of streamed movies is total crap. The Apple TV is the best of the junk streamers but still bad (I own 2) How does it sound if you play a blu rays?
Assuming it is the receiver (probably the source not the receiver) Does the receiver have pre outs for the mains? If so you could add a cheap used amp to drive them. There are some pretty good classe-d amps that are super cheap used. Not the best but it would give your speakers the current they need to get the bass drivers moving. 
I owned the 703s a long time ago and they need current and most receivers lack current even though they have wattage. And amp that doubles it’s power as the ohms drop is a good place to start. Like 100 watts into 8 ohms and 200 watts into 4 ohm is a sign of good current supply.