I think Yamamoto's correct on why the allies seem to strike first.
Matrix have discussed radar capabilities in several threads but good luck in finding them.
Here are quotes from two of them (from Erik Rutkins).
I believe the manual discusses this, but I'll paraphrase from memory... Surface radars have a chance of increasing the detection level of enemy ships. This makes the enemy easier to target accurately during a surface battle, particularly at night when detection levels are extremely low.
Air radar has a chance at giving early warning of an incoming strike, allowing more CAP planes to get to the right altitude and giving them a better chance of getting in a good fight before the strike reaches its target.
From deeper within the database... I'm not sure what Penetration represents in this case. I think Effect is related to the chance of it detecting a target.
Type 271, Range 28, Effect 75
Type 279, Range 250, Effect 70, Penetration 500
SC, Range 24, Effect 50
SG, Range 28, Effect 75
SJ, Range 25, Effect 70
CXAM, Range 150, Effect 50, Penetration 500
SCR-270, Range 250, Effect 70, Penetration 500
CPS-1, Range 400, Effect 80, Penetration 500
Type 13, Range 100, Effect 45, Penetration 500
Type 21, Range 20, Effect 55
Type 22, Range 34, Effect 60
What I can't determine is whether more ships with radar is better (I assume it is). It's worth noting that the type 13 radar is considerably inferior to the SG for surface combat detection. I assume its '43 in Oleg's game (when there are a lot more allied SG equipped ships).
If you want an opinion, I'd put them in your CV TF's and give yourself a better chance of protecting your high value ships by boosting your CAP effectiveness.
If you used the type 13 equipped ships in head to head surface combats, you'd still be operating under a disadvantage against the USN SG/SC ships in terms of detection effectiveness (IMO, one of the keys to success in surface engagements).
This is just a guess but the range of 100 for type 13 probably can't translate into an advantage in surface combat due to the way the surface routines operate (note the restricted range of the USN SC radar - it was primarily supposed to detect a/c - which should translate into a range closer to the Type 13 - as Matrix seem to be modeling it as a surface only, long range doesn't seem to be that important).
