the match between DD - CL comes to this:
- Researching them "costs" exactly the same. CL tech gives u better secondary armament as a bonus, and DD tech gives you better escort efficiency. it seems that any nation that can go the CV line naval doctrine (usa,jap) will build mostly carriers so secondary armament tech is insignificant to them. on the other hand better escorts for the convoys can have it uses (especially for usa).
- Building CLs are cheaper in icdays. However with 2 brigades attached instead of 1, CL costs the same as a DD. it's a draw.
- Brigades DD can have 1, CL can have 2 of them. it seems to be a clear advantage for the CL
- Air defence suits better for a CL, but once your fleet is getting bombed by naval bombers and you unable to cover them with fighters, it seems insignificant if your ships can shot back or not. Unfortunately CV's attack doesn't count as an "air attack" but a "sea attack" so the CL main purpose to prove better air cover versus carrier attacks, not modeled in this game. what a shame! still the CL shines better in this role.
- Submarine defence, DD suits better for this task. It doesn't seem so very important, never experienced a massive submarine warfare on the pacific. it's clearly more important to usa to counter german sub invasion. DD is much better in this aspect.
- In terms of Spotting and visibility DD has a clear superioirty what is very important in naval engagments, to determine the starting positions of the fleets.
- Speed, as Pang pointed out, CLs later in the game can't keep up with modern carriers. It is a very serious drawback, to reduce the speed of the whole fleet. DD is better.
- Supply/oil consumption. it is absolutely no matter for Allies, but could be more important for nations like Japan. DD superioirty in this aspect is clear.
- Repairs, DDs are cheaper and faster to repair, but they sustain higher str losses because of the lower "sea defence" capability. i don't know... call it a draw.
- Scavange of outdated models DDs can be converted to escorts once seriously outdated, while CLs has to be dismantled. it's a clear advantage of the DD.
So my conclusion is: any cv-heavy nation can use DD better than CL for screening purposes. On the other hand nations with lots of BBs and BCs constantly aiming for short distance naval engagements can have better use of CLs because the longer firing range / better punch they provide, and because of their secondary armament bonus on warships.
Please feel free to comment on this or correct my mistakes, or points left out from the analysis.