Jeepkid, how heavy is your Dakota? I assume you handload? This article below practically banished the thought of ever buying any .338 that is not the Win Mag, for me. But, unlike you, I have no experience shooting either cartridge, so I'm curious what your thoughts are about what Gary Zinn writes, here.
The TL;DR version is that performance comes at too great a cost in recoil, monetary cost of rifle, monetary cost of ammunition, and overall efficiency given the increased components necessary to get the difference in downrange performance.
http://www.chuckhawks.com/338win_vs_super_mags.html