I've done two Nilgai trips to the King Ranch as part of corporate group events and both were great. We stayed one night on property both times and had one guide per 2 hunters and each hunt was very different. First, they guarantee you at least a shot at an animal (at least they did for the 2 day hunt package).
The first trip I was the first shooter and my hunt lasted about 10 minutes as the guide spotted two bulls on our drive out to the area we were going to hunt. After about 5 minutes to get in to position and on the sticks I had a clean single heart shot kill at about 75 yards and the rest of my day was very enjoyably spent tagging along with the other hunter and stalking for hours until he got his animal shortly before sunset.
My second trip included a cull whitetail and Nilgai combo. The weather was completely different this trip and I was second shooter for the Nilgai and we drove pastures and stalked for a while and came up empty day one after spooking a bull we didn't know was there from about 30 yards. The second morning day I killed the white tail on the way to our Nilgai area and it wasn't so much hunting as harvesting, 100 yards under a feeder resting the gun on the truck side mirror. Not much exciting or rewarding about that other than being able to say you killed a whitetail on the King Ranch and helped manage the heard, it was a 6.5 year old 8 point that measured 122.5.
Not long after the buck, we stalked for a bit before finding a shooter nilgai bull. Had to get in to position and almost spooked him, but got a good shot off the sticks at about 100 yards. I hit this one a little back and instantly got nervous but quickly found him nearby with two vaporized lungs.
Others in our group had very different experiences, some with much longer shots and many others requiring multiple shots and varying degrees of chasing the wounded animal to finish them off.
All in all, the King Ranch is great and would absolutely recommend it for the nostalgia, top quality guides, and high likelihood of a successful hunt. I haven't been anywhere else, but I would imagine some other spots may be more "sporting" if that's what you are looking for.
My biggest piece of advice is to bring enough gun and only take a shot if you are comfortable as once you pull the trigger and hit an animal you're paying for it and they are tough SOBs. My first trip I shot a 300 Weatherby mag and had a 300 PRC for my second trip (that makes for a really clean/quick kill on a skinny whitetail at 100 yards). I think the King Ranch requires a 30 caliber magnum round or larger unless they know you and approve something else.

