IMO there is two separate issues to address with this question:
Firstly: the types of salt of a drug can have different physical properties that in the body can lead to slower or faster absorption. An example is Adderall which is pharmaceutical amphetamine and dextroamphetamine in mixed salt forms. Those different salts are meant to have slightly different kinetics I think, so different onset etc, which may 'soften' the total effect.
Also salts can vary in molecular weight, so even if they are just inactive/inert chaperones of the actual drug, they can be 'dead weight' that can affect potency. Hydrochloride is relatively light, so HCl salts are fairly potent.
Secondly: Salts are made up of a cation and anion (or a complex of several), so a positive and negatively charged. Usually the base is the drug, if the ionic acid portion is active itself! Such as in the case of valerate which is a form of valeric acid, then you have two drugs in one, bound together with ionic bond.
I'm racking my brain though why the phenibut citrate would be so different from hydrochloride, not only in kinetics but also pharmacodynamics? So even differering therapeutic action? Let me try to find something on that..
I think it's just the superior solubility > dissociation > absorption of the citrate - it very well must be since citrate from citric acid is not psychoactive. And it is cleaved from the phenibut almost as soon as it hits water.
http://www.ncbi.nlm.nih.gov/pubmed/22891435
But cannot read the full article