Though a Vaishnava, I feel advaita appeals to the modern mind, because it doesn't depend much on fairy tales, superstition, faith etc.
The modern mind refuses to believe in a creator, so if Vaishnavas tell him God is a blue-skinned person (and yes, he's got a name!), they're not gonna take it seriously. OTOH, comparing the world to a dream appeals to the modern mind, so much so several movies have been made on this fascinating theme.
As to pramana, it's virutally impossible to convince people of the reality of, say varaha avatar that lifted the earth. But to prove that the "I" exists as undifferentiated consciousness (which is what advaita is about) is easy because it's self-evident.
For these and many other reasons, advaita seems to tower over vaishnava and other schools of thought, despite Prabhupada and others doing so much to spread vaishnava dharma and krishna bhakti. The modern mind just can't accept these things, when the pull of advaita is so strong.
This is my observation, and I feel it will remain this way for some time to come.