You have to look at it in the big picture across the roles. The old classification is a pretty simple way to look at it.
Tanks- High defensive stats, can easily survive an assassin's bust, and can last a long time while being focused by sustained damage. Has low damage, but often high cc. Meant to be part of their team, protecting the carries while they do their work. Can duel assassins, but will probably not secure the kill.
Fighters- Medium defense and offensive dps, slight burst. Paired with tanks as frontliners, or roaming alone. Able to zone the enemy carry with their presence, and should be focused if fed. Is great at dueling any champ.
Assassins- High burst, low sustained damage and defense. Meant to remove enemy carries, and should reliably duel squishy champs. Able to dodge most strong cc, but is very vulnerable to point and click cc and exhaust spell.
Mages- Strong zoning in a large area around them, medium burst and dps, low defensive stats. Their damage is more reliable on immobile champs, countered by champs with strong engage, but able to kite others easily.
ADC's- Strong sustained damage, low defensive stats. Very reliable damage in a relatively small around them (this was changed and allowed the jhin/caitlyn/mf meta). Weak to engage, able to kite others it played right. Can duel champs with low damage relative to their tankiness.
ADC's are a middle-of-the-road role. Right now they are overtuned. They should be able to kill tanks, but not this quickly. A tank with 9x the effective hp as a squishy should take 9x as long to kill, not 3x. Assassins are squishy but should be able to kill the adc before they die themselves (as adc varus I nearly dueled a fed khazix shortly before the assassin rework). They should not be able to get the kill if successfully peeled, but barring peel, the assassin should win every time. Fighters with 2x the defensive stats and .66x the damage of an adc should win in a duel as long as they are not kited too much. Mages should out-kite the adc, but should die quickly if they get within aa range. The problem right now is that they can drain-tank the fighters, kill the assassins faster than the assassins can kill them, and shred tanks with items like bork and lord dominick's regards. Some can even out-poke the mages. The whole deal about too much burst relates to the fact that all champs have too much damage right now, and some have high damage nukes like Vayne Q.