The command to favor the changes in your local branch is:
git pull --rebase -X theirs
The reason why you have to say "theirs" when, intuitively, you'd like to say "ours" is because the meaning of "ours" and "theirs" is swapped during a rebase compared to a merge. Let me explain.
Ours and Theirs in a Merge vs. Rebase
When you do a merge, you're always merging into the current branch; in case of a conflict, "ours" means the branch you're on, while "theirs" means the branch you're merging. Exactly as you would expect.
A rebase is different. Let's say that you're rebasing a branch called local onto master.
master
⌄
o---o---o
\
A---B---C ‹ local
During a rebase, Git creates a sort of "temporary branch" to do the work1. It starts by moving HEAD to the tip of the branch you're rebasing onto, in this case master:
master
⌄
o---o---o ‹ HEAD
\
A---B---C ‹ local
Then, it cherry-picks the commits from local one at a time:
master
⌄
o---o---o---A'---B' ‹ HEAD
\
A---B---C ‹ local
Now, let's image that commit C has a conflict:
master
⌄ X
o---o---o---A'---B'---C' ‹ HEAD
\
A---B---C ‹ local
In this case, "ours" indicates the temporary branch Git is working on, while "theirs" is the branch from which the commit was cherry-picked, which is local.
If you wanted to keep the changes in your local branch, you'd have to choose the "theirs" side. If, instead, you wanted to keep the changes in master, you'd choose the "ours" side.
Once the conflict has been resolved, Git completes the rebase operation by moving local to point to where HEAD is:
master
⌄
o---o---o---A'---B'---C' ‹ HEAD, local
\
A---B---C
Given that no branch is left referencing commit C, those commits become unreachable and will eventually be deleted:
master
⌄
o---o---o---A'---B'---C' ‹ HEAD, local
1 It's really just a detached head, but for the purpose of this explanation, you can think of it as a temporary branch, even though no branch reference is being created.