As Greg says there is a difference between APS-C and Full Frame although it has nothing to do with the sensor size, it's all to do with pixel size.
I also have a Nikon D7200 which is a fantastic sensor BUT it does have smaller pixels than pretty much every FX sensor on the market. Let's take a comparison between a D7200 with a 24mm lens and a D810 with a 35mm which give a comparable FOV working from a 1.5x crop.
The D7200 has 3.91 micron pixels and the D810 has 4.88 micron pixels. This means that with a 24mm f/2.8 and a 35mm F/2.8 both wide open.
1) Same FOV
2) D810 has a 55% increase in pixel area for photon capture
3) D810 has higher resolution (28.75"/pixel vs 33.6"/pixel)
The D810 does this with 50% more pixels! So yes, a FX setup will outperform a DX setup if both sensors are good (they both are). Whether this is worth 5x the price tag is all up to you
