Note 4 is your best bet and if you are a really heavy gamer the Note 4 N910C Exynos is what you want, the CPU is similar to the S6, same GPU, but chip is built on a older 20nm process, but still Octa Core.
I would say overall the Note 4 is the best all-round smartphone out right now: incredible battery life, gorgeous high PPI display, 32GB built-in (25GB available) plus 128GB MicroSD slot, one of the best performing cameras around, great build quality etc... As a Note 2 user you probably know the great SPen features and multi window multitasking.
Had my Note 4 N910F Snapdragon 805 for 6months now and very happy. The S6 and M9 seem to have average battery life at best. The S6 is the fastest phone around while the M9 the hottest (literally, the Snapdragon 810 is quite the rushed job). I wouldn't get a phone with a Snapdragon 810 CPU, so either get a Note 4 or wait until the Note 5 drops with an updated Exynos and probably 4GB RAM.