I think the use of SARH or the Active homing is decided by the factor of operational requirement, both are basically the same, the disadvantage for Active radar seeker is it is guided by its own seeker right from the word go giving it fire and forget capability, since the radiating power of the missile head is much lower compared to mother ship or ground based radar it finds it difficult to illuminate the target while a larger more powerful radar helps in filling this gap till the missile reach too close to the target to get a better image of the target.
SARH & ARH are not one and the same. A SARH requires radiation from the GBR system for its receiver to pick up & home in on, whereas the ARH can finish the job (provided it can evade jamming) even if the GBR cuts out after a period of time.
Nor does it work this way - that the ARH is active from the word go. Well, that may work if your missile slant range is less than ~20 km, as the typical active seeker can lock on at that range. But mostly, how it works is the missile gets to a specified point using proportional navigation & INS/Command guidance inputs, and then switches to its onboard seeker for the end game. This is what makes it fire and forget (after a while).
While the advantage of Active radar homing is fire and forget capability, that means (in AAM mode) the jet fighter donot require to guide it thus escape the conflict zone once it is fired. SARH for SAM seems to be a better option as it have to deal with a variety of threats from small UAVs to new generation stealth fighters. While Active radar can be useful against ARM where the ground based search radars can be switched off to escape a ARM hit.
Fighters or any launch platform do have to guide the ARH because the typical seeker lock on range is around ~20 km. Even if you double that, add jamming & see the range reduce. Basically, how it works is like this - you detect the target, fire the missile, guide it to the range at which the seeker can get an assured lock, and then cut the guidance from the ground or the fighter. This means you can now remove the launch platform, radar etc from the engagement cycle. SARH on the other hand has a receiver only seeker which homes in on the reflected radar energy from the launch platform's radar or the ground based radar. So it has to keep the target illuminated throughout whike the SARH missile homes in. It was supposedly a more accurate method than seeker less missiles. In real life though, the SARH missiles like the Sparrow, AA-10 have had a lousy record.
The Akash employs command guidance to get near a certain range to the target, when its warhead explodes with an effective radius of around 2X that distance, giving a single missile a lethal SSKP of 0.88 (single shot kill probability). The BLR (Rajendra) has significant ECCM capability allowing for the missile to accurately hit targets employing ECM. The missile can then trigger its warhead based on its automated fuze, and if that is jammed, timed or manual intervention.
Overall, its a fairly decent system.
If an ARH seeker was to be employed, then the radar could cut out after the first 15 odd km of guidance. Might make a difference in terms of facing ARM equipped enemy's. But even so, the radar and control center are separated. That does give the crew decent survivability.