I have a mix. For me, I've tried to approach my "elite warriors" as being normal people (though highly trained and competent), but belonging to a special cultural group that are viewed a little in awe by regular people. I've modelled this on other historic "elite" groups that were alternatively lauded, feared, etc. The Hashshashin, Templars, Shaolin, and so on.
Most of my cultures have their own "elite" groups, each with its own unique characteristics and place in both its immediate community and the wider world.
Terrador's "Greycloaks" are the second sons of nobles, professional soldiers who man the fronteir, highly regarded by the commonfolk, but really not much more than regular medieval soldiers.
The hard desert-dwelling "Moh-Shadawahn" are unruly and independent mercenaries in the Samulian armies, universally feared and held in awe by allies and enemies alike. Their name means "Men of the Bitter Salt", and it's said they can't be killed because they give their hearts into the protection of their Shamans before they go into battle.
The "Herum" of the Ardveii continue an unbroken 2,000 year old tradition of warfare; proudly declaring in their name their own frailty.
The "Sadu-lan" of the Glaraheil are reviled by their people as thieves and murderers, but their skill and uncompromising dedication to the Goddess of Vengeance makes them untouchable. To the wronged, to those seeking justice, they are heaven-sent, faceless executioners of the Goddess' wrath.
The Phalagians are armoured knights of the Espallian Church, their namesake the Angel of Divine Vengeance, viewed in utter terror by all who live within the sway of the church. Many a village has burned at their hand, for the slightest infraction.
The Spectre Guard are an ancient, secret order, mindlessly and desperately clinging to preservation of a lost Empire destroyed a thousand years ago, but kept alive behind the impenetrable walls of their mountain fortress Teleportis.
And so on.