Choose Git merge strategy for specific files ("ours", "mine", "theirs")

Even though this question is answered, providing an example as to what "theirs" and "ours" means in the case of git rebase vs merge. See this link

Git Rebase
theirs is actually the current branch in the case of rebase. So the below set of commands are actually accepting your current branch changes over the remote branch.

# see current branch
$ git branch
... 
* branch-a
# rebase preferring current branch changes during conflicts
$ git rebase -X theirs branch-b

Git Merge
For merge, the meaning of theirs and ours is reversed. So, to get the same effect during a merge, i.e., keep your current branch changes (ours) over the remote branch being merged (theirs).

# assuming branch-a is our current version
$ git merge -X ours branch-b  # <- ours: branch-a, theirs: branch-b

For each conflicted file you get, you can specify

git checkout --ours -- <paths>
# or
git checkout --theirs -- <paths>

From the git checkout docs

git checkout [-f|--ours|--theirs|-m|--conflict=<style>] [<tree-ish>] [--] <paths>...

--ours
--theirs
When checking out paths from the index, check out stage #2 (ours) or #3 (theirs) for unmerged paths.

The index may contain unmerged entries because of a previous failed merge. By default, if you try to check out such an entry from the index, the checkout operation will fail and nothing will be checked out. Using -f will ignore these unmerged entries. The contents from a specific side of the merge can be checked out of the index by using --ours or --theirs. With -m, changes made to the working tree file can be discarded to re-create the original conflicted merge result.