"big_move" allows for a two pass alignment in 3dAllineate. The two-pass method is less likely to find a false minimum cost for alignment because it does a number of coarse (blurred, rigid body) alignments first and then follows the best of these coarse alignments to the fine alignment stage. The big_move option should be a relatively safe option, but it adds processing time.
The giant_move option expands the search parameters in space from 6 degrees and 10 mm to 45 degrees and 45 mm and adds in a center of mass adjustment. The giant_move option will usually work well too, but it adds significant time to the processing and allows for the possibility of a very bad alignment.
If your data starts out fairly close (probably the typical case for EPI and anatomical data), you can use the -big_move with little problem. All these methods when used with the default lpc cost function require good contrast in the EPI image so that the CSF can be roughly identifiable.