I don't think it's so important to relate the signal type with the antenna type. What's important is the signal that leaves the controller. Is it vertical linear polarity? That would be the stock antenna and many other antennas that are typically chosen to be modded onto the controller (ITELITE, Argtek, etc). So therefore you'd want a vertical linear polarity antenna on the bird side to match the control side, such as the one DJI already has on there. Obviously, you'd like the best one you can find. You need two for the 5.8 ghz signal and two for the 2.4 ghz signal.
So you have a p3S and you want to upgrade the stock antenna. You want to replace the stock antennas with the best possible antenna you can find.
I would not hesitate to replace the 2.4 ghz antennas with that from a P3A/P. I've heard and read that the results are very good. One of the long distance guys flew 19.4 miles linear distance with a stock P3P antenna on his P3P.
I would not replace the 5.8 ghz antennas with a P3A/P antenna because those antennas are not designed for 5.8 ghz. I would find another antenna or just leave it alone.
You might consider a P4 series birdside antenna, since those antennas are designed to deal with 5.8 ghz. You will need to research this.
I don't have a P3S, but on my P2 series ACs, I've used this:
5.8GHz Dipole kit for P2V+ Itelite panel - FPVLR
and I've even used this:
http://www.thanksbuyer.com/image/cache/data/201407/30670/1406340566-1-750x750.jpg
with very nice results - over three miles distance with trees severely blocking the signal (e.g. stock distance was rated only 500 meters on the P2V).
A few of the long distance guys are known to prefer circular polarity for the 5.8. If you want to do that, you probably want to also convert the controller antenna to a nice long 5.8 ghz CP antenna such as the super cannon.
Your flying environment will influence your decision on what polarity will be best to use.
Hope this helps.
