You need to clarify (mostly to yourself) what you are really asking:
a: Is the new disk subsystem much worse than the old?
b: Is SQL Server 2016 by itself somehow worse when it comes to I/O for tempdb?
c: Is your load on SQL Server 2016 (compared to 2008) causing more I/O on tempdb so much to that you push the disk subsystem and in the end see the latency figures you see?
The answer for b: is "No".
As you probably realize, we can't answer a: and c:. That is for you to determine.
For a: you take SQL server out of the equation and run a disk performance test on each disk subsystem. Make sure you run it under realistic conditions (your SAN might be under heavy load during daytime, so a fair comparison should be done at daytime, for instance).
For c: you probably want to compare the old and new SQL Server version with the same load and installed on the same machine and see if only the version of SQL server is what is causing the difference. Or perhaps you already have the answer, from question a:.