Tradition! (Cue the Fiddler on the Roof)
In 1E, they had the following stats:
Sword +1, Flame Tongue, +2 vs. regenerating creatures, +3 vs. cold-using, inflammable*, or avian creatures, +4 vs. undead. Sheds light only when its possessor speaks a command word or phrase, and this flame illuminates the area as brightly as a torch. Note that the flame from this sword easily ignites oil, burns webs, or sets fire to paper, parchment, dry wood, etc. Cold-using creatures are those whose attack mode involves cold (ice toads, white dragons, winter wolves, yeti, etc.)
Sword +3, Frost Brand, +6 vs. fire-using/dwelling creatures. Bestows the +6 bonus in a self-explanatory manner. The weapon does not shed any light, except when the air temperature is below 0 F, but it does give special benefits against fire, for its wielder is protected as if he or she were wearing a ring of fire resistance and whenever it is thrust into fires it has a 50% change of extinguishing them in a 10' radius -- including a wall of fire but excluding a fireball, meteor swarm, or flame strike.
Clearly, the Frost Brand has lost a bit of power, over the years. It originally (I have no experience w/ OD&D) was as potent against cold-based critters as the Flame Tongue was (+3) and was significantly better against its target foes. Plus, it had the resistance bit and the ability to dispel some magical effects.
Even in 5E, it's somewhat more potent, if not much. The difference between the two could be that they're just on either side of the line, with the Flame Tongue being 4500 gpv and the Frost Brand 6000 gpv (or whatever you decide). Those broad price ranges are just categories. I wouldn't expect a Frost Brand to range anywhere from 5,000 to 50,000 gpv. Instead, I'd expect it to be categorized as rare because it's assigned/list price was relatively static, but happened to fall somewhere in that range.
* Note: Gygax used "inflammable" synonymous with "flammable".