All of the monitors you're talking about have nothing much in common besides panel type perhaps. Asus doesn't make it easy, I don't blame you. I only started to learn this after being asked this a billion times at work what the difference is between X, Y, and Z.
The Asus
VN247H you have is apparently a 1ms TN monitor so they're completely different. The problem is that because its a 1ms TN monitor, the chances are that it is suffering from severe reverse ghosting. Reverse ghosting occurs when the manufacturer is too aggressive with overdrive/response time compensation.
Another possibility is that the monitor has some funky PWM frequencies that is some really neat multiple of 60. Two things you can try is turning the brightness to max and see if the ghosting changes. Also, dig through the OSD and see if you can find some "trace free" setting. Play around with the numbers but, generally speaking, Asus monitors have the best motion performance when it is set at 40 or 60.
Anyway, the monitor you have and the monitor that Digital Versus reviewed are completely different: the Asus VS247H is a completely different model from the VN247H. Furthermore, the Asus VS247H is completely different from the Asus VS247H-
P which is the model referenced in the OP. The fundamental difference is the model with the -P suffix has the trace free setting, which allows you to control the amount of overdrive/response time compensation you have. The model without the -P suffix does not have this.
If we're talking about alternative monitors to recommend, most of these cheap 60hz TN monitors are all kind of duds. There's probably a decent one out there but no one does proper reviews on them and so much of low end monitor market, amusingly, is all about marketing and specsheets. The availability of the trace free setting in the Asus VS247H-
P, at the very least, gives the end user the ability to fix whatever awful job Asus did regarding the default overdrive. This is the primary reason for the recommendation, though its possible that its a complete dud of a monitor as I haven't actually taken a good look at it.