Draining max HP can be frightening, but it has to be coupled with some heavy hitting bad guys in the following encounters. It is easier for the PCs to go unconscious in an encounter, and it can bring back the specter of a PC with low HP getting killed outright by devastating damage. Having the PC's max HP reduced means that it is easier for damage to hit their negative max HP.
Ability drain works, but it can create a bit of a bookkeeping nightmare. It is easiest to track a negative modifier to all rolls that use that ability (i.e. record that you currently have 2 less than normal so your +9 Wisdom saving throw is now +9-2 = +7) rather than changing the Wisdom numbers all over the character sheet.
In the process of converting the Age of Worms 3.5 AP, I ran into lots of creatures that caused level drain or Constitution loss. The ones that have a 5e analog did max HP drain, so I had the custom monsters do that as well. The PCs had to decide between using a precious spell slot for greater restoration (when someone even had that) vs. holding out for a long rest. In other cases, such as poison, I had the poison or other effect cause disadvantage on d20 rolls using that ability until the PC was cured.
Don't forget that negative levels went away after 24 hours, similar to how 5e removes the effect after a long rest. The difference is that 3.5 required a Constitution saving throw for each negative level. Failure caused a loss of an actual level. A close equivalent would be to have the PC roll a constitution saving throw for each hit die worth of max HP that needs to be recovered (maximum amount, so a d12 would be worth 12 HP). Failures do not recover that portion of the last max HP and the PC recovers 1 fewer hit die at the end of the long rest. The PC can attempt to recover the failed max HP again after another long rest.
By and large it seems to me that 5e resources are more limited than in 3.5 (at least the scale of modifiers is lower). That and the fact that most balance for monsters and PCs is done by a combination of damage and HP means that a PC with lower max HP is definitely at a disadvantage.