FujiFilm XT-1 or Nikon D750?

I'm looking into buying a new camera something on the lines of an entry level professional camera great resolution good low light pictures and profile style picture along with some landscape style pictures

Well lets see.

The Nikon D750 is a full frame camera, the sensor should perform better when it comes to dynamic range, colour depth and performance at high ISO settings.

Most of my friends who shoot landscape photography use full frame cameras or medium format digital cameras.

DXOmark.com has not tested the X-T1, so I have included the X100. It has a similar sensor (same number of pixels)

By the way, what is a "profile style picture"? Are you alluding to portraits? If so, I can tell you that I use a Full Frame Nikon D800e when shooting group and portrait shots.

What's a profile image? Are you talking about the small images people use of themselves on social media?
Anyway, since you're interested in landscape photography, without question get the D750. Better yet, save your pennies and get the Canon 5DS R instead. In between would be the Sony A7R II, which if I had to do things over again, I'd go with that over my Pentax 645D purely for the low weight and immense assortment of lenses.

These are two different classes of cameras. The Fujifilm XT-1 is comparable to the Nikon D7200. And Fujifilm does not have a class of camera that compares to the Nikon D750. Both of your chosen cameras are capable of what you intend to use them for, so it is a matter of how much you want to invest and what feels good in your hands. The Nikon D750 would be an excellent long term investment.

"Entry level professional" sounds terribly wrong when put together. Entry-level refers to budget. Professional means the person gets paid for his services.

I expect the XT-1 to blow away the D750 in low light shooting. Apart from that, you can use either camera in shooting anything that you can think of. Picture quality will depend on your skill. The camera is only a tool.