The "wahhh! Wizards are more powerfull than warriors" spiel has been an ongoing fallacy for decades now in D&D.
The fact is that Fighters out DPS wizards in about every edition. Wizards have more versatility. But thats really it.
The main factor for fighters is getting ahold of magic weapons and armour. If a campaign is stingy on the items then the fighter can end up falling behind a bit. But not by much. The system is alot more balanced than most give it credit for.
The problems start when people begin to remove the restrictions on casters.
We must have been playing a completely different 1st edition version of D&D then. Because there is no way any fighter can compete with fireball and mobs of goons getting hit with it on the DPS meter. But I think that was balanced with the squish of the wizard and the difference in XP to level.
It depends on the level of the fighter and what kind of weapons they have or options are being used in the game. Granted, I only played 2e and used a lot of options, so "disclaimer", but the highest level (lv 20+ at some point) longest running fighter in my old 90s gaming group had max STR and dual-wielded twin Scimitars of Speed +5 with scimitar weapon mastery and the guy could ditch out ridiculous damage per round, between STR bonus, magic weapon bonus, and mastery bonuses, plus like 5+ attacks per round due to level, mastery, dual-wielding mastery and permanent Haste from the scimitars. All of which adds up to enough damage rival a Fireball (1d8+STR+Magic+Mastery x5+) if all attacks hit (which they always did at his level, plus bonuses). And he could do that Every. Single. Round. No bullshit spell slots or anything, but... Every. Single. Round.
We also used Called Shot rules, cuz "realism", and with his effective THAC0 from all his bonuses plus class level he could decapitate (-8 to hit, called shot to the Head) almost anything as a routine roll. Called Shot rules just break apart at higher levels older editions of D&D (anything before 5e, maybe 4e, really) because THAC0/Attack Bonus keeps improving and magic bonuses rack up to the point where a -8 to hit (the highest penalty for called shots, which is to the head or vitals) becomes negligible. At least for warriors.
But that's a matter of whether you allow those rules or not. And a lot of this depends on what type of magic items you allow in the game. A warrior without magic weapons is gonna be at a serious disadvantage against a magic user at higher levels. This makes warriors highly reliant on gear just to measure up to casters, while spell casters need no weapons still ditch out serious damage or buff themselves up.