Magic swords in Original Dungeons and Dragons were far more potent that most people give them credit.
That is doubly true when using the Chainmail combat rules, rather than the "alternative" (d20) combat system. That alternative, d20 combat system diluted the power of those magic swords, and it, along with the innovation of hit points, were a baleful influence on future versions of D&D.
Remembering that the Chainmail combat rules were ODnD's original, default rules, this quote from Chainmail gives some indication of how magic swords were first viewed by Gygax as he penned ODnD:
"Magic Swords: because these weapons are almost entities in themselves, they accrue real advantage to the figure so armed. In normal combat they merely add an extra die. It is in fantastic combat the magical swords are most potent. Besides allowing Elves to combat certain fantastic figures, they give a plus 1 to the dice score when employing the Fantasy Combat Table, and Magical Swords shed a light of their own over a circle 12" in diameter (6" radius) which dispels darkness but does not equal full light. Excalibur and other 'super swords' would give a plus two or three!"
-- Chainmail, p.38
"Merely" adds an extra die? In mentioning the addition of an extra die, Gygax refers, of course, to the use of d6's, in Chainmail's normal (mass) combat rules, to determine the chance of wounding one's opponent. Using Chainmail's normal (mass) combat rules, and assuming both combatants are "armored footmen", either combatant needs to score a 6, on a single d6, to wound his opponent. The combatant with the magic sword, who adds an extra d6, needs to roll a 6 on either of his 2d6, and therefore has a 31% (11/36) chance of wounding his opponent, while the combatant, without the magic sword, has a 17% (1/6) chance of doing the same.
Put another way, that +1 sword, in ODnD, is actually a +3 sword, if you were to convert the odds of wounding over to the alternative, d20 combat system (you need an 18+ on a d20 without the magic sword, or a 15+ with the magic sword). Add to that, the 3% (1/36) chance that the magic-sword-weilding-combatant will score two wounds, and that humble +1 sword looks potent indeed!
Gygax's reference to the "addition of an extra die in normal combat" is more problematic (and potentially powerful), when you consider its application to Chainmail's man-to-man combat rules. Taking the "addition of an extra die" at face value, you could interpret this to mean you roll 3d6, instead of 2d6, when consulting the man-to-man combat table. Again, assuming the employment of our ubiquitous +1 sword, against an opponent with Plate Armor and a Shield, our odds improve from 11+ on 2d6 (3/36 or 8%) to 11+ on 3d6 (109/216 or 50%).
Again, converting this to the alternative, d20 combat system, that +1 sword actually improves my chances of wounding my opponent, from 19+, to 11+. My +1 sword just became a +8 sword!
Even if you dismiss that extreme interpretation, in favor of a more reasonable +1 to the dice score on the man-to-man table, your run-of-the-mill +1 magic sword is still very potent. Against Plate, your odds of wounding improve from 17% to 28%. Against other types of armor, your odds improve from 42% to 58%. Those odds turn that simple +1 sword into a +2 or +3 sword, when converted to the alternative, d20 combat system.
I see no evidence in ODnD that magic swords were considered to be anything but the puissant and dangerous items suggested by the Chainmail rules. In addition to the above combat bonuses, there was a 50% chance that a magic sword would have sufficient Intelligence to have a Will of its own, which it would attempt to impose upon its wielder:
"Swords: among magic weaponry, swords alone possess certain human attributes. Swords have an alignment, and intelligence factor and an egoism rating .... If the Intelligence/Egoism of the sword is six or more points above that of the character who picks it up, the sword will control the person ...." -- D&D Volume II, Monsters & Treasure, p. 27
This was the case, even of the lowly +1 magic sword. Indeed, those +1 swords had a 50% chance of having some special power, a 25% chance of talking, and 17% chance of reading magic or having some other extraordinary ability.
The most powerful sword bonus in ODnD was +3, and for good reason. A +3 sword would truly have been the equivalent of an Excalibur or Stormbringer, particularly if the sword had high intelligence, ego, and several extraordinary abilities to boot. The dilution of the magic sword, first, by the introduction (without adjustment of the odds) of the alternative, d20 combat system, and second, by the introduction of hit points and accompanying applications of 'bonuses to damage' instead of additional wounds, along with a host of additional features to add "granularity" to D&D, led us to the current morass of +16 Swords of Valiant Smiting and Characters with 40 hit points at first level.