Well, 'Matchbox' were relatively new, being more known for their '00' or 1/76th scale die-cast cars, and entered the kit market as the first to introduce recessed panels lines, albeit rather heavy recessed panel lines. They had a huge range of kits, mainly 1/72nd scale, with a very few in 1/48th and 1/32nd. But their range included a heck of a lot of more 'unusual' types, and were, generally fairly good, although with a strong aim at the younger market, with multi-coloured parts.
Airfix we know about, as the first mass-producer of plastic kits, some of which are still going.
Frog produced a wide range of kits, again, including some of the lesser know types, all in 1/72nd scale, apart from a brief venture into the then new 1/32nd scale market, the examples of these now being still part of the Hasegawa range.
Their 1/72nd scale kits, for the time, were very well moulded, with fine detail and interior details in the form of seats, instrument panels, and control columns etc, something which, at the time, Airfix did not do, apart from a token effort on some of their larger kits. Although some items lacked detail in parts, for example turret guns, they were more to scale and very fine, and some of the landing gear legs, for the time, were nicely detailed, as were the canopies, with well defined, engraved framework.
To me, Airfix seemed to be substantial in 'feel', although perhaps not always truly accurate, and perhaps sometimes 'heavy' in appearance of exterior detail, whereas Frog could look somewhat 'light' in appearance, but very nicely moulded, and not as thick in such areas as side walls and gear doors, for example.