First, what happens when you are level drained? According to the rules (2E DMG, pg. 73):
"The character's experience points drop to halfway between the minimum needed for his new (post-drain) level and the minimum needed for the next level above his new level."
Note the word "halfway". In other words, a 10th level fighter who gets hit by a wight drops down to 9th level. However, he only loses half a level (technically). He would drop to half way between 9th and 10th.
A fighter needs 250,000 xp to hit 9th level and 500,000 xp to hit 10th level.
So let's say our hero just hit 10th level and has exactly 500,000 xp. A wight hits him. He does not drop down to 250,000 xp. Instead, he is now half-way in between. He has 375,000 xp and needs just 125,000 xp to regain 10th level, not 250,000.
With things like spectres and vampires it hurts more, but even then it's a matter of losing 1.5 levels, not 2 levels. Our 10th level fighter gets hit by a vampire and he drops to halfway between 8th and 9th level.
Now, how harmful is this to the character? Well, a few less hit points, maybe a thaco penalty, if a wizard perhaps a few less spells memorized. So for awhile, the affected (drained) character functions and goes on adventuring at a slightly lower level than normal, and gradually - with no expenditure of magic, treasure, or wealth - he becomes his old self, totally restored.
However (and this is the most important point), that is all self-correcting! All of those problems and penalties are fixed by doing nothing other than what the character would do anyway...go adventuring!
In contrast, let's look at petrification.
First, being petrified immediately takes the PC out of play. He doesn't continue playing/adventuring at a slightly reduced level. He is simply a worthless (if well adorned) statue. He must make a system shock roll from the stress of being turned to stone. If that fails, he is dead (even if someone later manages to turn him back to flesh). Even if the system shock roll is successful, the petrified character in any case needs someone with access to a stone-to-flesh spell to turn him back into living flesh. Assuming he makes yet another system shock roll, which is needed to survive the shocking transition from stone to flesh form. And if he fails that one, or the earlier one, then in either case he's going to need someone to get him to a cleric who can cast raise dead. And if they can't get his corpse to a priest in a few days, he's out of luck and stays dead. Assuming they do reach a cleric of high enough level to raise him there is the issue of alignment. Is there a church of proper alignment that would even be willing to raise him? And if so, how much are they going to charge...because it certainly won't be free! Considering a regenerate spell to replace a lost limb costs 20,000 gp (DMG, pg. 113), I'd say the cost for raising the dead is at least that high, maybe double that. And even then, the character is probably going to be bound to a quest for the favor. Once the spell (raise dead) is cast, the character now needs to make a successful resurrection survival roll. If that fails, he's forever dead.
If any one of those things are not available or fail...a stone-to-flesh spell, two system shock rolls, access to a cleric of proper alignment with the ability to cast a raise dead spell within the short time frame, a successful resurrection survival roll, lots of cash, and the agreement to go on a quest...the character is finished. Roll up a new one.
Even if he accomplishes all this and is raised, he loses a point of CON, perhaps has fewer hit points, and is less likely to survive a future shock or be raised again. Plus, when he is raised he has just 1 hp and needs days (perhaps weeks) of bed rest. AD&D is not 3E. You don't jump up out of your death bed and go into combat. You have to rest and recuperate.
And just how the hell did they manage to get that 1,000 lb. statue out of the dungeon and back to town to the wizard who can cast stone-to-flesh?
Being petrified really sucks!
How about artificial aging? Assuming the character has been adventuring for years and has reached 10th level, he is likely in his late 20's at the very youngest, and more likely in his 30's or 40's. A ghost touches him, aging him 30 or 40 years. Now he's in a much older age bracket. If he hits 60 years old (and likely will) he loses a point each of DEX and CON, and two STR points. This can adversely affect his thaco, damage bonus, ability to open doors or bend bars, lessen his ability to lift and carry things, makes him easier to be hit in combat, makes him more vulnerable to surprise, penalizes his abilities with missile weapons, lowers his hit points, lessens his ability to survive system shocks (petrification, aging, etc), and makes it less likely he can be raised from the dead.
Worse yet, unless he has access to a potion of youth (or a rare wish spell), the aging is permanent. There is no de-aging spell in AD&D. A potion of longevity only restores at most 12 years and on average just 6 years. Probably not gonna make much difference.
People no longer recognize him, there may be marital issues, etc. Lots of role-playing aspects affected by this.
And even just dying from getting gored by an ox or breathed on by a dragon entails all the issues listed above concerning being raised from the dead.
So why do people whine about level drain so much? Why do they go through crazy contortions trying to "fix" (i.e. diminish) the effects of level drain? I've never in all my years seen an "alternate" rule for level drain that comes close to the real thing. Every "solution" just waters down the effect of level drains.
My guess? Level drain isn't glamorous. You don't see anything. You're not burned to a crisp by dragon breath, turned into a statue by a medusa's gaze, or trampled under the feet of the mighty tarrasque. It's just more subtle. It feels like the character is going backwards (ie must re-cover lost ground).
But so what? It sucks, yeah, for sure. On the other hand, it is far less harmful, debilitating, or career-ending than being petrified, aged, or even killed by the numerous ways one can die in AD&D.
I just don't see the problem with level drain.
I would argue that makes even less sense than standard level drain in the first place. 
It doesn't matter what the rules clearly say, or what Gygax (who created the damned game) says, they refuse to agree. It's so pathetic there that they actually argued to defend an obvious and totally illogical typo in the 2E MM that says vampires exist on both the Positive and Negative Material Planes at the same time. Or that mummies get their power from the Positive Material Plane even when that makes no sense because: