Your studio recordings have been engineered by a pro no doubt with a heap of experience and tons of nice toys at his / her disposal. They've also had the time and control to adjust the individual sound of every member of the band to fit it all together well. A top notch live engineer would probably get you pretty close to the nirvana you seek. It would however need a solid pa system with a good mixing desk. Most portable pa systems will struggle unless they're a high end set up with subs, tops, 1000s of watts, rta Eq system, nice mic pre's etc etc etc.
A very good start for you if you're using a decent pa system would be something like a sansamp bass driver pedal or similar.