I've enjoyed the series of posts from Microsoft on the ways in which SQL Server 2016 was improved and is faster. Some of these posts show improvement without any change in your code. Some showcase features that might require change, but will bring about improvements, and after all, wouldn't you rewrite some code if you knew you could get performance improvements? Most of us would, if the changes are fairly simple. I know some changes are hard, but that's our job as developers: make systems run better, even if it's work to change our code.
Some posts are just fascinating. The one on log stamping, which highlights something I had no idea about. I wouldn't think that stamping 0xC0 is better than 0x00, but I'm glad someone dives deep into hardware changes like this. I know many of us don't have more than 8 CPUs running our databases, but we might at some point. Having a better way of ensuring soft NUMA works well automatically is good. Even if you don't care about how this works from a practical standpoint, it's an interesting look at how Microsoft is keeping up with hardware advances where a single CPU these days can encapsulate more than 8 cores.
SQL Server 2016 is not only the best version to date, but it's also the most tested and evaluated. Apart from all the evaluations and writeups performed on the CTP 2.x's , CTP 3.x's, the RC's, much of the code has also been running in Azure, where metrics have been gathered and evaluated for quite some time. There's at least one feature I've been hearing about for over 3 years, since well before SQL Server 2014 was released, at which time it was running in Azure already. In all that time, there have been lots of tuning and tweaking to ensure that the code is running as efficiently and effectively as possible for this release.
Note that I'm not saying that the product is without bugs. While some people think there's no need to wait for SP1 (I agree), I also think you should test thoroughly for your situation. It is entirely possible that there will be some bug that affects your code. And you need to test with actual systems and code. Also, be aware that there are documentation updates being made constantly, as we find that bugs also exist in BOL.
While SQL Server 2016 is faster than previous releases, there are quite a few new features that do require code changes. However, if you can take advantage of those features, I think it's well worth the development effort and the upgrade cost. Let me know what you think.