I also used to think having that having FF would be better especially low light. After I'm using my D7100 for almost one year, I feel i'm confortable with the noise as long as it doesn't surpass ISO 6400. So far what I thought in my mind is probably having FF would be great for sports and action due to very large buffers (except some DSLR like D800 etc). But for others, APS-C does the job incredibly well.
The short answer is yes, FF will always have an advantage for some things.
But i) are you going to notice it or do you know what you're looking for
ii) are you shooting in conditions where the difference is significant or can you make use of the advantage.
The truth is the current crop of sensors of all sizes are very good, good enough to the extent that it handles a large portion of ppl's needs with relative ease.
But if you have specialized needs eg. trying to freeze action on a sporting pitch with poor lighting or shooting black cats in coal mines then maybe its a different story.
BTW: you shouldn't look at noise alone when considering high ISO performance. Colour accuracy and saturation degradation as well as loss of DR are big negatives that NR won't help much with.
Personally I'd mainly consider FF for the 'look,' ie. perspective and DOF but that's cos I don't shoot at the edge of the performance envelope. Its not necessarily better (sometimes worse actually), just different from other formats. Just as medium and large format have a different 'look' again of course.
I'm facing this question too before I decide ff or crop sensor.
But in the end I chose ff.
D800E / Tamron 28-75mm f2.8 / 150-600 Tamron
Thanks for all your advice. Now I'll focus on DPP, a new area to learn.