In third edition D&D and its various spin-offs, spellcasters became more powerful than ever in mid- to high-level play—when compared to non-casters—to the point that “Linear Warriors, Quadratic Wizards” has become a perennial topic of discussion on gaming message boards. This is less of an issue in OSR gaming in that old-school rulesets predate the big power boosts of 3e, where more spell slots, broader spell selections, combat casting, and other benefits wound up eclipsing the skills and feats offered to non-casters. But the specifics of power balance between casters and non-casters varies significantly by ruleset even under the OSR umbrella, based on caster limitations and non-caster strengths.
In Moldvay B/X, “spells cannot be cast while performing any other action (such as walking or fighting).” (Moldvay Basic, p. 15) The limit on “fighting” is ambiguous; it could mean you can’t cast while attacking, or that you can’t cast while engaged in melee.
In Mentzer BECMI, “The caster must be able to gesture and speak without interruption to cast a spell. While casting a spell, the [character] must concentrate, and may not move. A spell cannot be cast while the character is walking or running. If the [caster] is disturbed while casting a spell, the spell will be ruined, and will still be ‘erased,’ just as if it had been cast.” (Moldvay Basic, p. 25) Again, it’s unclear whether simply being in melee or being targeted by an attack counts as ‘an interruption’ or ‘being disturbed.’
The first edition AD&D Dungeon’s Master’s Guide has an entire section labeled “Spell Casting During Melee.” In this ruleset, a character can’t take any other action while casting a spell. Not only does damage ruin a spell, so does dodging! “The spell caster cannot use his or her dexterity bonus to avoid being hit during spell casting; doing so interrupts the spell.” (p. 65) Furthermore, intelligent enemies recognize how powerful magic is and will go after spellcasting PCs to disrupt their spells.
Meanwhile, fighters gain a variety of abilities at higher levels in some OSR rulesets. In Moldvay B/X, “for every 5 levels above 15th, the fighter gain another attack that round.”1 (Moldvay Expert, p. 8) At 12th level, fighters in Mentzer BECMI gain multiple attacks and special moves such as disarming. (Mentzer Companion, p. 18) Fighter-types in 1e AD&D get multiple attacks as they gain levels, and when a fighter is fighting creatures with less than one hit die he gets a number of attacks per round equal to his or her level. (1e PHB, p. 25) 2e AD&D provides even more ammo in the form of weapon specialization, which provides ‘to hit’ and damage bonuses with the chosen weapon type. And all of the TSR old-school rulesets offer high-level fighters lots of followers and access to badass magic swords, both of which are invaluable in that style of play.2
Even so, old-school spellcasters have always been stronger than non-casters at higher levels. We see this right from the start in OD&D: “Top level magic-users are perhaps the most powerful characters in the game, but it is a long, hard road to the top.” (Men & Magic, p. 6) Newer OSR offerings, like Adventurer Conqueror King, have baked in fighter-only benefits like extra cleaving attacks and bonuses to damage and retainer morale, or—as with Lamentations of the Flame Princess—diminish the melee utility of casters to help fighters stand out.
Here are some blog and forum discussions proposing interesting fighter bonus abilities:
Fighters & Weapons (Untimately)
Thoughts on Fighter customization (Dragonsfoot)
 I suspect this should read “At 15th level and every 5 levels thereafter.”
 I have not listed OD&D because I find the combat system too impenetrable to assess.