The datasheet says 4A, the seller's text says 4A. However, I doubt it will push 4A without exploding.
I would not run that at more than 1A maybe 2A without additional heatsinking. Then, when you do have adequate heatsinking, I still would not run it at more than 3A max.
The LM2577 version has been around the net for a while, lots of people have posted in their blogs and here on the forum about their troubles with it not surviving.
It's $1.51 and free shipping. Just buy one and characterize it yourself. I just bought one. I'm curious too.
If I wanted to use it in anything I really cared about, I'd put it on a test bed and run it for up to 6 months on dynamic loads to give it something to be afraid of.