They are tough animals, and most importantly their vitals are placed high behind the shoulder. The traditional whitetail shot placement is likely a gut shot and causes a lot of running you hear so much about. I shot one on the Mariposa is South Texas a few years back. They were skitish and stayed in the heavy brush like an axis deer. I was on a whitetail hunt when we ran across a nice trophy bull. The only shot offered was a front facing neck shot at about 250 yards, as he peeked up and out of brush. I put the crosshairs right at the base of the neck and my 270wsm 130gr dropped it in its tracks. Looked like someone simply pulled the power plug.
My co-hunter shot one the next day behind the shoulder with a 300 weatherby 180gr fusion bullet and it ran for about 100 yards before it fell. I think it all comes down to shot placement. I do know that the ranch has a minimum caliber required of a 30 cal magnum. I just happened to have taken my 270wsm that day for whitetail. When we ran across it the guide told me to use his 300wm, but I told him I'm more comfortable with my own gun. He then told me if I shoot and wound it, I bought it regardless of the outcome. Luckily it all worked out!
I wouldn't overthink it. Nilgai reputation is kind of like wild boar. People also think you need a cannon to kill boar and talk about how tough they are, but you can kill them from anything from a 22 cal up, with right shot placement. Good luck to you on the hunt!