personally, I don't think there is nothing wrong to marry a grand complication with a lot of diamonds.
If you were offered two "identical" grand complicated watches (one with diamond and one without) for the same price, which one would you choose?
---- the one without diamond without a second thought because most value of a highly complicated watch is its MOVEMENT! Not its case, diamond, etc... OR
---- the one with diamond (without a second thought too) because it is good value;
I am none of the above... I would have a look of the watches first to see if the diamonds go well with the watch. If yes, I would pick the diamond one; otherwise, just the one without...
Of course, there is no way to have the same price for the above two watches.... usually, the market is asking for a unreasonable price for high-jewelry watches... so our impression is that ALL diamond watches are not worth the prices.... but does it mean that all watches (even grand complication) with diamond are bad?
For 5971P, the diamonds go so well with the watch... so I would pick it over the 5970. However, 5004 is a different animal...
Just my 2 cents 
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