I'm not even sure if the Chinese S-400 purchase includes 40N6.
There is just no way the Chinese military would purchase the S-400 without the 40N6, which is definitively the star of the S-400 show. In fact I would argue that it is in your court to show that the Chinese military DIDN'T purchase the 40N6 with the S-400 rather than on the rest of us to show that it did.
HQ-9 system is more similar with Patriot/PAC system than it is with S-300. The resemblance is the Chinese program thought the vertical launch and mobility of S-300 was far superior to Patriot and worth copying. HQ-9 is not simply a 1:1 S-300 PMU copy and has been developed into many different versions. For one thing, HQ-9 trial in Turkey was claimed by the trial to be the only system that hit every target. If S-300 is the same, it would have achieved the same results but none of the others managed it.
While I would agree that the H/HQ-9 has probably since evolved into a much different beast, it undoubtedly can trace its ancestry to the S-300 system, just as the H/HQ-16 can trace its ancestry to the Buk system, and the HQ-17 to the Tor system. Meanwhile the Patriot has evolved into a largely TBM-oriented missile system with significantly degraded AAW capability.
For PLAN, 052D+ and 055 (if not also 052C and 054A) do need to catch up to ESSM/SM-2/SM-3. Navalising S-400 will give PLAN destroyers an SM-2 equivalent if current HHQ-9 variants do not perform to S-400 level. Honestly China doesn't really need an SM-3 equivalent for now because it doesn't need to worry about rogue nuclear nations attacking it. SM-3s are pretty much only effective against NK or the like, so PLAN may want to focus on better anti-sub and anti-surface weapons rather than a ship based BMD.
Just a nitpick, but navalizing the S-400 would give PLAN an SM-6 equivalent, not an SM-2 equivalent.
Well, it's clearly just my opinion that the 052Ds are quite a bit more capable than the Burkes. I also don't deny that it is hard to know for sure, and if your opinion differs, then that's fair enough.
This opinion does not seem to be well-supported so far.
Sensor suite: While it is impossible to know the sensor capabilities of the SPY-1D vis-à-vis the Type 346A, the fact that one is a PESA and the other an AESA is not automatically a reason to give the advantage to the 346A; software is also important (perhaps paramount) to MFR performance. It must also be noted that the actual size of the 346A must be considered in the context of the fact that it is a dual-band MFR, meaning that the actual FCR (C-band) portion is MUCH smaller than what that panel suggests, just as the volume-search (S-band) portion is also smaller than what the size of the panel would at first suggest. My opinion is that we cannot give the advantage to either system.
ASuW: LRASM is on the fast-track to naval deployment, perhaps by 2019 (it is already EOC on B-1Bs this year), and once that missile enters service the YJ-18 will not give the 052D any advantage in ASuW. In fact I would argue that the LRASM is actually a generation ahead of the YJ-18. In addition, the SM-2IIIB and ESSM are both suspected of having secondary surface attack capabilities, while the SM-6 is explicitly stated as having such capability.
AAW: AAW goes solidly to the Burke. The 052D does not have a known ESSM-equivalent in deployment. SM-2MIIIB probably outranges the HHQ-9B while SM-6 definitely outranges the HHQ-9B.
ASW: Flight IIA Burkes have two ASW helos while the 052D has only one. OTOH the 052D has VDS/TAS while TACTAS was removed from the Flight IIA iteration. So it's not clear to me which one has a definitive advantage in ASW.
Point Defense: the only category which favors the PLAN. UNLESS of course you factor in ESSM as a point defense weapon, which actually the USN counts as such (despite its 50+km range) since the introduction of the ESSM was the stated reason the USN started removing Phalanx from their Burkes.
Magazine size: definitively favors the Burke. If I ever see evidence of a dual-packed HHQ-9, I may be tempted to call this category a wash, but until then there is just no contest here.
