The answer to the headline question is yes, it is equal. It physically has to be equal, since you can't have two different values of a particular directional stress at one point.
The quoted equation is for shear stress, where
V = total shear force at the location in question;
Q = first moment of area 'beyond' the point considered;
t = thickness in the material perpendicular to the shear;
I = Moment of Inertia of the entire cross sectional area.
The problem seems to be the assumption that the cross-sectional area above and below the neutral axis is equal (ie, the embedded question "the area both above and below the Neutral Axis should be equal ... is this statement correct" to which the answer is no)
Neutral axis is the line about which the first moment of area each side is equal, not the line about which the areas each side are equal.
Applying that equation above and below the neutral axis, V an I are properties of the whole section so identical wherever you do the calculation on this cross-section, t is a function of the level at which the calculation is done so identical in both applications, and Q is equal by definition (that's the definition of the neutral axis), so the answer has to be identical since all the numbers substituting into the equation are identical.
Example: for the diagram shown, if T=10, W=60, H=70, then the tee shown has a cross-section of 1200, and both flange and stem each have area 600. However, the neutral axis is NOT at the bottom surface of the flange (ie, is not where there is equal area above and below). In this example, the neutral axis is at 22.5 from the top surface, or 12.5 below the level at which the areas are equal either side. So there's 725 area above the neutral axis, and 475 below the neutral axis.
Calculating for above the neutral axis, there are two rectangular regions,
Q = 10 x 60 x 17.5 + 12.5 x 10 x 6.25 = 11281.25
Calculating for below the neutral axis,
Q = 47.5 x 10 x 23.75 = 11281.25
I = 552500 and t = 10 at the neutral axis, so whatever value of V is used, $\tau$ is the same.