I would definitely use intarsia for the white part of this pattern as well. Check out the intarsia how to video on this site, under the Intarsia Knitting section
You could do the black as intarsia, also. Or as a duplicate stitch after you finish knitting. From the picture, it looks like the original is done with the black as a duplicate stitch. Here is an excellent tutorial on duplicate stitch
(though I'm not a super fan of the finished sweater...).