Yes and no. War elephants are roughly comparable to flamethrowers in that they have tremendous psychological effect and, under ideal circumstances, they can be highly effective. However, their inherent limitations meant they were rarely decisive and never became battlefield mainstays.
We'll start with the advantages of the war elephant. Some of these are self-evident: it's an enormous, loud animal that can really wreck an enemy front line. This was particularly the case if an elephant was armored and had its tusks enhanced, such as with sharp metal points or iron flails (as was common in South Asia.) Elephants are highly intelligent and could even be trained to use these weapons. The psychological impact of such a large creature charging toward one's army could by itself achieve a rout. They had other less obvious advantages, too, including providing a surprisingly stable platform for archers. Outside of direct combat, elephants could also be used as pack animals themselves.
The drawbacks of the war elephant were many, however. One was logistics: ancient & medieval armies had to provide food and water not only for their troops but also for their animals. Elephants, as one can imagine, require quite a large volume of both. Elephants are prone to panic, and full elephant freak-outs in the midst of battle was not unheard of; the elephant then became a threat to its own army. Elephants, even if armored, were also vulnerable to attacks from below by spearmen (the classic "rock" to cavalry's "scissors".)
Like flamethrowers, war elephants ultimately offered enough advantages that they remained on the battlefield for quite some time, despite their drawbacks.
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