How to review a major revision of a paper?
When a major review has been requested, I think you really do need to go through the whole paper, for exactly the reasons you cite—the changes you've requested may conflict with the changes another reviewer has requested, and therefore the authors may have had to exercise significant discretion on which one to formally include in their revisions. Similarly, there may have been other changes that arose from your comments or those of your fellow reviewers. 

Minor reviews require a lower level of commitment, unless the authors have indicated more substantial changes have been made.