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I prefer inline, but I think mature code review solutions let you pick whatever you want anyway, like Crucible.

I could go either way. I've used both where I work, and I haven't found that one works particularly better than the other. In most cases, inline is sufficient, you can get the gist of a change (especially a one line change) just looking at them inline instead of a full side by side window. In the case of a real big, messy, merge-y diff, you're gonna have a rough time with either style.

Inline diffs are good for small changes here and there throughout a file. They are pretty worthless for large changes to a file (eg. heavy refactoring).

Bitbucket (and probably Github, too?) uses inline by default on pull requests but has a button to show a side-by-side and another to see the actual file.

Yeah, good point. We have got side-by-side diffs planned for future releases.