L-theanine is an excellent mood stabilizer. Effect wise, it really belongs in the same category as lamotrigine or topiramate, not with anxiolytics like benzos. But unlike most prescription mood stabilizers, it's extremely well tolerated and seldom produces toxic side effects even at many times its therapeutic dose. Though its chemical structure is not like any other known mood stabilizer, L-theanine's mode of action probably shares the familiar antagonism of the glutamate pathway of excitation.
L-theanine is an amino acid. Like all medicines that are amino acids, it should be taken on an empty stomach (approximately 1h before or after a meal), or at the very least with a stomachful devoid of any protein -- when I take it, I mix it into black espresso, with nothing else going into my belly at the time. Otherwise other amino acids will compete for absorption in your intestine, and much less will be absorbed.
L-theanine indeed does take the edge off caffeine and other stimulants, and potentiates dissociatives a bit, IME.
I highly recommend purchasing L-theanine in bulk from wholesalers if you like it and plan on using it often. If you purchase it pre-packaged in capsules, especially at a physical store, you'll soon find it a barely affordable habit. The best theanine in the world (some users claim it's the only one worth a damn) is the SunTheanine™ brand, containing only the levo enantiomer in a high degree of purity, made in Japan, where L-theanine was first isolated from the tea plant and is a popular food additive today.
L-theanine has a mellowing effect on harsh flavors when used as a food additive. It can be used as a flavor enhancer like monosodium glutamate, except that it does just the opposite -- blunt strong flavors instead of jazzing up bland ones, while imparting an unintrusive savory note in either case. This makes sense; glutamate is an amino acid too, and savory taste receptors' ligands are amino acids. Straight up, it has a strange and distinctive savory flavor, with a slight bitter-sweet finish, not at all unpleasant. It wouldn't surprise me if L-theanine was an ingredient in a number of successful chefs' secret recipes.