Bloomberg reports that Samsung has gotten weary of the random overheating problems that the TSMC foundry is facing with Qualcomm's Snapdragon 810 production, and, since it has superior production capabilities, decided to go with the latest Exynos for the S6. Who can blame it, considering that the company is having a brand new $15 billion factory built outside Seoul, which can churn Exynos chipsets in the tens of millions no sweat, which will be the likely sales numbers of a flagship Samsung phone, instead of relying on older production methods that on top of that TSMC hasn't apparently ironed out just yet. It's not the first time we are hearing that Samsung has given up on the unreliable supply of Snapdragon 810s, too.
Now, when it comes to what the differences are between Snapdragon 810 and Exynos 7 Octa, we'd have to wait and see exactly what modification Samsung has eventually used for the S6, but one thing is for certain - it will be built on the superior 14nm process, whereas Qualcomm uses 20nm for the 810, and only this year will move down to 14nm. In general this means less power consumption and smaller processor footprint and/or superior performance at comparable clock speeds, but Qualcomm has other aces up its Snapdragon chipset sleeve.
One of the advantages used to be its excellent multiband LTE modems that it paired with the Snapdragon SoCs, but now that Samsung created an LTE Cat. 9 radio of its own, that point becomes somewhat moot - more so it will be built on 20nm, whereas Qualcomm's LTE radio is still at 28nm. As for the Snapdragon 810 optimization for 4K encoding, decoding and streaming - it remains to be seen how Exynos will fare with those, though we wouldn't worry too much about it, as Samsung's chips have proven capable enough so far.