I'm also pondering over Nexus 7 FHD and Note 8 and Tab 3 8.0 last time.
In the end I went with Note 8, due to the MicroSD card and LTE, the S Pen, well, even I'm currently in studies, I don't find myself using it as much, usual Pen and A4 paper are still much preferable lol, especially to take down notes and drawing of diagrams, S Pen aren't "there" yet.
Tab 3 8.0 is a good alternative if you don't need the S Pen, almost specs, it's a tad slower than Note 8, due to dual core and 1.5gb ram, but you won't notice it unless you are stressing the CPU, other than that, the smaller bezel and of course cheaper to get.
Nexus 7 FHD, the only reason I find myself in getting this is the FHD screen, but other than that, nothing interest me. 7 inch is too small for me, also without LTE and MicroSD is so headache for me.
Note 8:
Best out of the 3 in terms of productivity.
S Pen
Note taking
Quad core
HD screen 189ppi
2gb ram
MicroSD up to 64gb
LTE
Phone call capabilities.
Tab 3 8.0:
Great if you don't need the S Pen over Note 8
Dual Core
1.5gb ram
HD screen 189ppi
MicroSD up to 64gb
LTE
Phone call capabilities.
Nexus 7 FHD:
Beautiful 1080 FHD screen 330+ ppi
Faster quad core
2gb ram
No S Pen
Better optimisation with Google
No LTE
No MicroSD
No phone calling capabilities.
Listed out almost all of the differences, have a read through and decide.
PS: There's bound a 2nd gen Note 8 coming out next year, roughly March or May, with upgrade specs like FHD screen and Snapdragon 600 or 800 I hope. But it's gonna be priced back to $800. Depends if you need it now, for the S Pen, if not, if you just want the 8inch form factor, can wait for LG G Pad 8.3