Like it is said before,
I find a J2 and J1 to be very close in economic balance. Taken everything together, from simple IPC-value of territories gained/lost, to NOs and PUs (value of units lost in the battles) lost or gained. I do find J1 to be more difficult and dangerous: Japan has a shortage of land units around Yunnan and they can make more mistakes that seem minor but are not. For example, if Japan takes their CA as loss if the BB in SZ37 scores a hit, the UK can be aggressive (attacking FIC) and Japan looses its offensive initiative early already, due to the mentioned lack of troops. I learned this the hard way the first time I tried a J1 ;-): Japan must take an air loss here. Just a small example.
But enough little details. If Japan knows what to avoid, they can make a J1 as good as J2 no problem. I consider it unwanted however, if my Japanese partner always wants to do J1 and does not want to do, or know how to do a J2. Or even a J3/J4DOW. If we are assuming no mistakes fom any Major power and friendly dice for all, Germany looses the option of doing SL with a J1DOW and their Barbarossa may be halted very soon as well, if the USA puts a little effort into the Atlantic (but never enough to loose the Pacific war!).
Global strategies are very situational and even Japan and Germany should at least make a plan together. If the axis want to try an economic victory, a J1 is not the optimal choice. If Germany wants to keep the threat of a SL open for a while (for whatever reason), J1 is far from optimal. And so on and etc. etc.
So, I’d say the DOW J1/2/3/4 really depends on what strategy Germany and Japan have agreed upon, and what they can see is the allied reaction to their plans.
A J4DOW can even be more profitable to Japan (and the axis as a whole) if they do it right, even to the balance of economy… There are certain conditions that must be met, ofc, but Japan can spot them in the early turns.
I consider it a strong player’s mark; the ability to know when to best do the JDOW considering the overall axis strategy and allied responses. And that is not always a J1. Well, unless the axis never try a different strategy together. Which play into the allied hands because you 'll become too predictable ;-).
J1 is as strong as any without a doubt, but its biggest strategical downside is that it gives away Axis intentions early and even takes away certain axis threats that would otherwise remain in place, requiring more cautious play from the allies.