Every luminous object's flux and luminosity obeys the inverse square law.
So if we compare two objects - let's call them A and B - then 

                          (L of object A)
   (F of object A) = --------------------------  and  
                     4 * pi * (r of object A)^2


                          (L of object B)
   (F of object B) = --------------------------  are both true.
                     4 * pi * (r of object B)^2


Let's use F(A), L(A), r(A), and F(B), L(B), r(B) in our notation to
keep things shorter.  Now, if F(B) = F(A), then the relations can be
combined to produce a new relation:

       L(A)               L(B)                 L(A)     L(B)
  --------------- = --------------- , or just ------ = ------ .
  4 * pi * r(A)^2   4 * pi * r(B)^2           r(A)^2   r(B)^2

So if A is twice as far away as B [ that is, r(A) = 2 * r(B) ], which
object is more luminous, and by how much?  Well,

      L(A)          L(B)
  ------------ = -----------; so L(A) = 4 * L(B).  
  (2 * r(B))^2     r(B)^2

On the other hand, if A is twice as luminous as B [L(A) = 2 * L(B)],
which object is more distant, and by how much?  Well,

   2 * L(B)      L(B)
  ---------- = --------; so r(A)^2 = 2* r(B)^2, or r(A) = sqrt(2) * r(B).
    r(A)^2      r(B)^2


Now we can get a bit more complicated.  Let's say the flux you measure
from A is five times more than the flux you measure from B, but you 
know their luminosities are the same.  Let's further say that:
   right next to A there's a star with a flux of 500 W/m^2, and
   right next to B there's a star with a flux of 100 W/m^2.
Which star is more luminous?  Well, F(A) = 5 * F(B), so

     L(A)     5 * L(B)
    ------ = ---------- ; and since L(A) = L(B), we can deduce
    r(A)^2     r(B)^2


   5 * r(A)^2 = r(B)^2  so  sqrt(5) * r(A) = r(B).  

   So the star near A has luminosity 

        L = 4 * pi * r(A)^2 * 500 W/m^2.

  and the star near B has luminosity 

        L = 4 * pi * ( sqrt(5) * r(A) )^2 * 100 W/m^2.

Apparently, according to our calculations, the stars are equally luminous!
We come to this conclusion without knowing what r(A) and r(B) actually may
be; it only matters what they are relative to each other, if we carefully
use the inverse square relationship between flux and luminosity.