Most of the 'true' hallucinogens are classified as 5HT2A agonists. 5HT2A is a postsynaptic serotonin receptor. Serotonin-specific reuptake inhibitors (SSRIs) on the other hand act by increasing serotonin (5HT) levels in the brain, which in turn activates presynaptic 5HT1A receptors. Due to a continuous stimulation of these 5HT1A receptors they become downregulated (Hjorth et al., 2000).
5HT1A receptors are crucial for the negative feedback loop that controls 5HT release from the raphe nucleus neurons. When they release 5HT, they will postsynaptically activate a myriad of targets, but also presynaptically activate 5HT1A receptors, which inhibit 5HT release. Continuous 5HT1A receptor stimulation through SSRIs downregulates the 5HT1A receptors, thereby disrupting the negative feedback and resulting in a continuous, disinhibited flutter of 5HT release, in turn leading to overall elevated 5HT in the brain and suppression of depressive symptoms (Hjorth et al., 2000).
Among the most well-known 'true' hallucinogens we have LSD, mescaline, psylocibin and dimethyltryptamine (DMT). All of these are thought to act as 5HT2A antagonists (Nichols & Sanders-Bush, 2001) and do not elevate mood. Although they may induce euphoria, they may well induce a state of terror as well, dependent on the nature of the 'trip', which heavily depends on the acute mental state of the person ingesting the drug.
The one class of hallucinogenic drugs that may act as an antidepressant from a neuropharmacologic point of view is MDMA (ecstacy) and related compounds (MDA, MDEA etc). These drugs can, arguably, be classified as a hallucinogenic, although their hallucinogenic properties are far less pronounced as compared to mescalin and LSD. MDMA and related compounds evoke massive 5HT release, among other effects and induce acute euphoria, and virtually never dysphoria seen with the 'true' hallucinogens. However, after the effects wear off, a backlash typical for these drugs may be experienced, reminiscent of a dysphoric state associated with a burning out of the 5HT in the brain. Therefore, its effects are too transient to be classified as antidepressant. Long-term MDMA use is associated with brain damage (Fisher et al., 1995). Short-term euphoria is also seen with dopamine-agonists like amphetamine, meth and cocaine, drugs associated with even more severe comedown ('crash') after the effects wear off.
To wrap up, and answer your questions:
1) Are hallucinogens anti-depressive agents? - No.
2) Which are their advantages and problems in comparison with modern antidepressants? - They act too shortly by inducing a few hours of euphoria, after which a period of dysphoria follows. Long-term use of MDMA and related compounds will lead to insomnia, addiction, and brain damage which are unwanted side-effects. Hence, these illicit compounds are not suitable for replacement of regular antidepressants.