The Compare tab of DirSync Pro:

Compare file sizes and modification dates. With this option, the file gets copied:
when the file in Dir A is modified later than the file in Dir B (in case of New/Modified copy options), or:

when the file is Dir A is larger than the file in Dir B (in case of Larger copy option).

Compare file sizes, modification dates and meta data (attributes, permissions, ownerships): With this option, the conditions from the previous option apply, plus that the file meta data is taken into account. The file will get copied if the modification data is changed (New/Modified copy option), file size is larger (Larger copy option) or attributes/POSIX permissions/POSIX ownerships are changed.

Compare file contents: with this option, the file contents will be compared byte by byte if the file sizes are the same. If file sizes differ, a sync conflict will occur. Please note that comparing file contents is a very time consuming task.

The Conflict Resolution tab: shows options when conflicts happens while using a mono-directional or bi-directional synchronization. You may set these options only if the Sync Mode is set to bi-directional or a custom mode.

Mono-directional conflict resolution tab.

Mono-directional sync conflict resolution through Overwriting the file in destination with the file from the source: when synchronizing from mono- directional in a custom mode, if the file in destination is modified later (file is newer), the file from the source is copied over the file in destination; the file in destination will be overwritten.

No Mono-directional sync conflict resolution Do nothing. Just warn me: when synchronizing from mono-directional in a custom mode, if the file in destination is modified later (file is newer), nothing will be copied. Instead the user gets a warning and could fx the conflict manually.

No Mono-directional sync conflict resolution Do nothing. Just skip silently: when synchronizing from mono-directional in a custom mode, if the file in destination is modified later (file is newer), the file will be skipped silently.