Mark in Paris[Purist]
10488
It is indeed quite a difficult choice
and as such, you'll have very different and interesting inputs to help your decision making process. Keep in mind that we all represent a specific part of the watch population and that it is more about guiding you through your own process 
First, as it seems the 5970G is new in your final stage of decision, I would really suggest you keep taking your time (what you're obviously doing and that is good). Especially since they are so different and can't be easily compared.
It will all come down to what you like wearing, your clothing style, life style, when you wish to wear it, how often, the comfort, complications you like, etc...
As mentionned above, the budget is significantly higher for the 5970G.
The 5170P has a beautiful and modern dial, it works fantastically with the diamond markers and the white printings. I think that this kind of dial is not usual (different tones of blue) and that the case makes it comfortable, well sized etc...
The diamond issue is for me a great asset of the watch. It will need time (and nobody has to accept them anyway) but I think that they will become "cool", contemporary and bring the watch in a very different category of watches. Not better or worse but just in a separate section for the ones you can't describe regarding the usual standards.
There has always been diamonds on watches, not with the same meaning and I think that today's for such a dial, it is again something else (i.e. new). It seems that it even appeals to younger clients. Of course, we don't know either how it will evolve in the future. As every aesthetical elements, it will depend on how it will be supported in future models by brands, by who it will be worn, if you see them in other fields etc... it will be the same for 2-tone watches or yellow gold.
As for the 5970G, it is a more "secure" choice. It is much more classical and "under the radar" with the all grey look and darkened elements.
The movement, the complications, the case and bezel (oh I like that bezel too Thomas, certainly why I also like this 5960), the good balance, regarding today's standards, between traditional and more contemporary etc... are making this model a true reference on every level.
Personally, I don't know which one I would pick... Maybe the 5170P because of lower budget and the dial that attracts me more but not very sure yet (I had a look at it too). That's why it is very personal.
On the one hand, a fantastic and unusual novelty, while completely in the standards of the brand, that will hold imho a very interesting place in the chronograph lineage and, on the other hand, a very successful model, gathering very appealing complications, with a recognized historical place concerning the caliber and the whole model's design.
Keep us informed
Best, Mark