Rapidly increasing TempDB write latency
Looks like the disk subsystem on Server B is performing worse than on Server A but, I used to see disk issues not entirely related to disk specs. You could collect some other performance counters such as physical disk --> avg disk sec write (> 25 ms very slow), memory --> page file usage (> 70% bad), cpu --> processor queue length (> 12 very bad), memory --> pages/sec(> 600 slow, > 2500 very slow disk subsystem), sql server: buffer manager --> page life expectancy (&lt; 300 memory issue). 

You can also limit the growth of 6 tempdb data files to the size they have now. See what happens. 

You should check the waitstats as well on both servers. If you see a lot of PAGELATCH_XX then you will know where to dig more. Jonathan Kehayias has a good article on this theme. And Paul Randal has also a lot of analysis which could help.