Please elaborate on how sensors ARE or ARE NOT balanced between ships and stations in the current game, give me numbers and hard math please?
I will provide you with numbers because you asked, but I will not endorse any particular balance argument. It is my opinion that sensor ships are perhaps a bit on the strong side but not an issue of the proportions which you and several others in this thread appear to believe. Targeted exploration with fast scouts is still a viable alternative to wide-area exploration with sensor ships.
A ship with sensor range R can see a number of tiles N at the start of its turn, where
N = 3*R^2 + 3*R
not including the tile in which the ship resides. A ship with sensor range R can reveal a further number of tiles Q with each move action, where
Q = 2*R + 1
though it should be remembered that Q is not the same as the number of tiles for which the ship's movement has revealed new information. A ship with sensor range R and move actions per turn M can therefore provide you with current knowledge of up to T tiles per turn, where
T = N + Q*M
It should, however, be noted that the information thus obtained is not guaranteed to be unique, nor is it guaranteed to be new. Assuming a static map, the maximum amount of new information a ship with a sensor range of R can obtain per turn is Q*M. If you have two ships with sensor ranges R1 and R2 and movement per turn M1 and M2, then if N1 > N2 but M1*Q1 < M2*Q2, it will take t turns for ship 2 to surpass ship 1 in terms of number of tiles revealed, where
t = (N1 - N2) / (Q2*M2 - Q1*M1)
It should be remembered that this is not, strictly speaking, a good measure of how useful a ship is for exploratory purposes, as this doesn't evaulate whether or not the tiles revealed are tiles that you already had all the desired information about or not.
A ship (ship 1) with M1 moves per turn, R1 sensor range, and an x turn head start on some ship 2 with M2 moves per turn and R2 sensor range can begin exploring tiles that ship 2 cannot reach yet after y turns, where
y = (R1 - R2 - x*M2) / (M2 - M1)
under the assumption that both vessels are moving along the same path and started from the same point. To put this in perspective, the survey ship that you start with on turn 0 can by turn 8 or so begin exploring areas that a sensor ship which was rushed on turn 0 and became available on turn 1 cannot yet reach, while the scout ship you start with on turn 0 can do so by about turn 18, assuming that the scout/survey ship and the sensor ship both follow the same path. Movement bonuses can shift the time slightly in a way which favors the faster ships, and being smart and not sending your ships all out along the same path will also help out (a move-2 ship with 4 sensor range which you start with will begin to reveal areas which the sensor range 24 sensor ship you got on turn 1 didn't cover starting on turn 10 if the two ships are traveling on paths which are sufficiently different from one another, i.e. the scout is not paralleling the sensor ship from well within the sensor ship's sensor range; speed bonuses will improve this somewhat).
The big sensor ships are good at exploring lots of area quickly, but they're not necessarily that good at exploring the right areas quickly. You know roughly where the planets are because you know where the stars spawned, and if those stars are more than a certain distance away you'll find out what's there more rapidly by using a faster scout ship with more limited sensor range than you will by using a slower scout ship with a larger sensor range. Sensor ships are therefore good for exploring regions close to the shipyard rapidly and for efficiently searching large regions, whereas fast scout ships are of greater value for rapidly searching distant areas of limited size which are expected to contain something of value (e.g. the area around a known distant star).