I own a number of Atlases and, as a double star fanatic I am very much interested in their usefulness with respect to these objects. I place the Millennium Star Atlas far,far above the others for these reasons:
1. The plate scale is the largest of any atlas which greatly assists star-hopping and also estimating RA and Dec.
2. The vast number of pairs indicated. Thousands of pairs.
3. The symbols used to indicate the pairs gives an approximation of the separation and a very accurate representation of the P.A. The length of the single thin line emanating from the star is proportional to separation while the line actually points in the direction of the P.A. All of the other atlases just indicate a pair with a thin line through the star.

A good night's observing would be simply to pick a page and attempt to observe all the pairs on that page. Make some notes as to RA, Dec and your anecdotal observations. The next day you can go online to the WDS and look up the data for each pair you observed the night before.. The bonus with this method is that the data in the WDS is always the most up-to-date available, rather than the static data in the lists published in books.
Of course, the Millennium Atlas is also the most expensive one out there..... I have no doubt that, in this case, you get what you pay for.