I honestly don’t know enough about the different HID models or anything to know offhand if the NExT will work immediately with it, but I’d probably air on the side of yes, if I had to guess.
Both the iclass and iclass SE readers support 14443A. So should be no problem with the xNT/NeXT. Although they do have to be configured in Security mode 1. Mode 2 or higher are iClass only and will not support the xNT chip as it requires an encryption key exchange. The multiclass readers will be a problem for the NeXT as it will excite both sides of the chip.
Any of the ancient ProxPoint readers are a breeze and will work no problems with the xEM portion of the NeXT.