Now add the typical constitution bonus, and yes, you probably end up with three times the hit points.
Regarding the hit points, my 'three times' came from the fighter being more likely to have a constitution bonus. 9*d4 = 22.5 9*d10+1 = 58.5, or close to 3 times as much.
In 1st edition AD&D, the fighter is not much more likely to have a high constitution modifier than is the magic user. Both fighters and magic users prioritize one score (Strength for fighters, Intelligence for magic users) before a couple of "secondaries" (Dexterity and Constitution), and both of those secondaries go before the rest of the scores. The order of those secondaries is more of a personal choice than a systemically encouraged one. At 15 constitution, both fighters and magic users get +1 hit point; then at 16, both have +2. It isn't until a 17 constitution score that the fighter has an advantage, which is magnified further at 18.
If given the choice, magic users will end up with a high-ish constitution, just like a fighter. Of course, if there is no choice (any of the methods where you can't arrange your scores to taste), then it is pure chance as to who gets the higher score. The low end of the scale is slightly more interesting, as a fighter has a minimum constitution of 7 (no penalty), while a magic user has a minimum constitution of 6 (which nets a -1). (If you went with Illusionist in 1e, you'd have a definite point, as they must have a minimum dexterity of 16, forcing their priorities.)
In 1e, then, unless you are dealing with relatively generous rolling methods (such that the fighter ends up with a 17 or 18 constitution), you are likely to have the same constitution modifiers for hit points per die. Variation here is more due to whether the player prioritizes dexterity for AC adjustment or constitution for hit points, and by luck for what scores were rolled. (Perhaps even just luck, if no re-organizing scores to taste is allowed.)
In point-buy 3.x edition, both are likely to assign a 14, netting +2 constitution modifier. In fact, my experience is that a wizard is more likely to prioritize that, as adding +2 basically doubles their hit points per level, while it is only adding ~1/3 to the fighter's average.
I think a fairer statement is that fighters are likely to have slightly more than twice a wizard/magic user's hit points.
A further fair statement is that a wizard/magic user has a great number of additional options for avoiding hit point loss in the first place, though (through stoneskin, protection from normal missiles, etc.). Yet another is that the wizard/magic users are the only ones that can, under their own "power," alter their attributes above and beyond whatever leveling gives you (by virtue of the wish spell and/or magic item creation).