For a typical jump the drug is safer than a low berth. Suspended animation in a low berth would be similar to travel via fast drug (muscles, drying out, etc). Some safety factors need to be incorporated with each.
You would have no need for staterooms for a fast drug passenger. All your need are basic seats. The tonnage from a stateroom would accommodate a dozen or more passengers. More if you has them lying down and you stacked them.
Fast drug has an advantage since you could use it in an emergency, whereas you would need to already have the low berths installed aND functioning.
It's not a panacea, and there probably would be drawbacks to using the drugs that aren't mentioned.