Considerable cost? You are either a REAL tightwad, poor as a proverbial churchmouse, or buying from the wrong company.
CPM440V Military's can be had for $100.00 all over the place these days. The lowest I've seen the ATS34 models was $89.00. That's only an $11.00 difference.
I got my CPM440V for $95.00. If the Military in question is an old model vs. new model, then spend the extra money. If it's just a steel vs. steel argument, then buy whatever steel fits your needs. I have a lot of experience wrapped up in sharpening ATS34, but not CPM440V, so I don't know what one is "easier." Theoretically, the ATS34 model would sharpen faster, but the CPM440V would hold the edge longer. CPM440V is also more stain and rust resistant than ATS34. That's a bonus for me becuase I sweat like a horse and am very corrosive.