The short answer to your question is: it depends.
![Grin ;D](http://aurora2.pentarch.org/Smileys/classic/grin.gif)
Overall, you need to break down a couple of concepts: Detection and Targeting (Illumination).
Once you've done that, you need to identify usage. For instance, in your home system, DTS may handle most of the detection anyway, while in other systems, you don't want to rely too much on Active Sensors for detection but probably on Passive ones.
Finally, if your fleet is scouting, staying undetected is probably best suited, making the AWACS emissions an easy target to spot from distance. If you are actively looking for trouble instead, then the AWACS would help to ease your ships from sensors tonnage, and that tonnage can be redistributed to firepower or extra layers of armour.
In my opinion, having a dedicated ship for both Detection and Illumination is a good strategy when you don't have a clear strategy against an unknown enemy or are looking for a broader approach, as it allows you to tailor your strategy as you encounter new enemies with enough warning to react. One ship (AWACS) could help with detecting enemies from far away and even initiate active tracking. However, if, for instance, I use 5m km missiles, I typically include a 10m km Active Sensor (AS) as redundancy on the assault ship, along with the fire control system. This redundancy ensures that in the event of the loss of an AWACS, the fleet maintains its detection and combat capabilities.
Further down the road, once you have a broader understanding of your enemies, you can design relatively inexpensive sensors with the sole purpose of detecting and targeting specific ship classes from a safe range, avoiding their potential barrage. This could render the AWACS a luxury in terms of Build Points (BP) and Maintenance costs, and, from one perspective, a liability. You should consider using Fighter or FAC Scouts instead at that point.