Software/Hardware Upgrade
Run the same query on a backup on both systems that matches production as closely as possible.  Show us the queries, execution plans, execution times, and perfmon counters.  This is the best way to find out what's happening.  I'm sure we can see what's going on.  During 1 DB migration I had a major networking issue with a firewall pegged at 100% CPU between the web servers and SQL.  End user experience was horrible, and NETWORK_IO was the highest wait stat, so maybe it's not SQL Server related.

I recently went from 2x E 4core / 48gb ram to 4x E7 8 core CPUs /256GB ram and saw some interesting results as well.  

I had to tweak:
-Parallelism threshold and set maximum parallelism setting per query.  Check your 
SELECT *
FROM SYS.DM_OS_WAIT_STATS
ORDER BY 3
Seeing CXPACKETS way high won't mean you have a parallelism issue, but I found it helpful to increase the threshold and CXPACKETAS fell from #1.