This is a darn good question but I doubt if anyone has detailed comparisons between the two. I can speculate that the BR-136 has a fat 1/4 wave element for 700-900MHz range that is coaxially mounted around the whip giving these antennas a fat base. Then the single whip probably resonates as a 1/4 wave on VHF and 3/4 wave on UHF giving a good match but an upward skewed radiation pattern on UHF. Then the BR-137 seems to have a coil in the middle, probably a 1/4 wave phasing coil for UHF possibly making it a stacked colinear of some kind and adding a little gain at UHF. This is just my speculation.
Browning is not considered a high end brand and for about the same price as a new BR-136 you can get a brand new Laird version or one sold with Harris or Motorola multiband radios sold surplus on Ebay and they are of higher quality. I bought a couple of Laird brand versions in the $40 to $50 range new and they are usually well over $100.
I've tested the Laird version of the BR-137 against a Larsen Tri-band and a COMPACtenna and the results were interesting. They all have good and bad points, but to me the COMPACtenna seemed to have more good than bad of the three tested. You can read some of my testing here.
Comparison, Larsen Tri-band, Laird WPD136M6C-001, COMPACtenna Scan III - 118 to 922MHz
