GABA is a calming inhibitory neurotransmitter. It is the brains natural Valium.
Some theories suggest that depression is due to too little serotonin, whereas anxiety is due to too much. Buspirone is a kind of "two-fer" when it comes to serotonin--that is, buspirone is a partial agonist (a substance which initiates a physiological response when combined with a receptor). This is a drug that acts as a kind of weak stand-in for the native brain chemical. So, if the person has too much serotonin, buspirone competes with this chemical and effectively dilute its effect on nerve cell target sites called receptors. If the person has too little serotonin, buspirone can step in and give these serotonin receptors a little kick, so to speak. (In high doses, buspirone appears to have antidepressant properties).
Although GABA is the brains primary inhibitory neurotransmitter it is common today to prescribe antidepressant drugs that increase serotonin (SSRIs) to treat anxiety
 The fact that serotonin increasing antidepressant drugs can be helpful at relieving anxiety symptoms indicates both that serotonin deficiency may be involved in anxiety and that brain chemistry is very complicated. 
One of the main reasons that antidepressant drugs are being prescribed for anxiety is that compared to anti-anxiety medicines they have less side-effects, they are less addictive and less likely to cause harm if accidentally or deliberately over consumed. To be frank compared to antidepressants research and development of useful anti-anxiety medication is in the doldrums. 
Serotonin increasing antidepressant drugs take up to 4 to 6 weeks to begin relieving symptoms of anxiety and therefore cannot be used in the same "as needed" way as theanine can. The amino acid tryptophan can boost serotonin levels overnight. Therefore the natural remedies are quick acting and enable you to fairly quickly test the efficacy of boosting either serotonin or GABA.

Stimulated brain centre - Caffeine