Bob, I own two of the "Browning Hawkens", one in .45, and the other in .50. The correct nomenclature for the Brownings is the Jonathon Browning Mountain Rifle. The intent of Browning at the time was to produce a rifle that looked more authentic than the T/C Hawken, or the T/C Renegade. IMHO, they succeeded very well. Both of mine are very accurate, and they get a lot of good comments at the range. The browning of the barrel, and the pewter nose cap add to the authenticity. They are a little heavy with the barrel length, and the fact that the barrels are 1" across the flats. That just adds to the stability, again IMHO.
Depending on the condition, $350 is not a bad price, and you may have been able to dicker a little. I've seen them go for as much as $600 on various auction sites. The commemoratives will go for as much as $1000.
Best always and make smoke,
YMHS Dennis