I have one of the Monoprices. They have a few models now.
Where they differ from Apple is quality control; some have pixels off. But many vendors have policies about those, and outfits like Monoprice are super good about returns. Maybe better than Apple...I don't know their dead pixel policy.
You also miss maybe ethernet or USB ports. BFD; easy to get those anyway, assuming you need them, and maybe you don't need them.
The other brand monitors may not have the connections you need; as price goes down you may get only one type of connection, like DVI or HDMI. If your card supports that you save a bunch; lots have display port connections. As noted previously, however, that HDMI port can come in handy with lots of stuff. And Thunderbolt is nice, but do you really need it? Kind of a waste if you can run the monitor some other way, like just DisplayPort. And 4K? really diminishing returns for most people.
Some don't have really nice stands. The monoprice one I have has VESA mount holes (and they sell umpteen million mounts) and a good sturdy stand. Just happens to sit about 1.5" below my very similar (but inferior) 27" iMac screen (which has dust contamination, hence is inferior).
The most serious downside, IMHO, is the collection of monitor controls you may get. I couldn't adjust some stuff on my monitor as easily as with some other third party or Apple monitors, but in my case where I'm using it means I don't care. It's basically set up to be exactly like the iMac, so it works for me. Others need more control. Here's an example review of the panel I got (note that the actual panel may differ in what monoprice or others sell now):
http://www.tftcentral.co.uk/reviews/achieva_27_ips-zero-g.htm
If your a pro who needs things like exact color calibration and have the tools to do so, you need to do your due diligence to see if the monitor can be adjusted to your liking. Best to ask in forums where people do that kind of calibration to see what each is capable of before you buy, whether it be Apple or any other. And what works in the light where you work can differ as well.
For many of us, a cheaper alternative like the monoprice I have just works for general stuff; I don't have to do color calibration in any fine detail. Using this monitor over Apple's saved me enough to get a better graphics card. So YMMV. Maybe Apple, but maybe it's a waste of $$. Frankly, for the current price of an Apple Thunderbolt display you could probably get a used 27" iMac that you could use in Target Display Mode, and have some backup computing power to boot. And maybe it would have a bluetooth mouse and keyboard.