Nothing bad, if you use "bup" or "borg"; The latter has better delete support, so is a better choice for rolling backup if you sometimes delete data. "bup" has the advantage that its repo format is git, which makes it easier to hack.
Both use rsync-style deltas to only send changes, but they use a content-addressable scheme like git so renames are a small metadata change record.
Also, both offer ftp and fuse interfaces if you need to access an older backup.
Bad things! rsync isn't smart enough (AFAIK) to know that files have been renamed or moved: it just sees files disappearing on one side and appearing on the other side, so the daily delta can get big.
DRBD may be a good solution to this problem, although I haven't spent the time to see what it would take to replicate over ssh, and the kind of traffic that is incurred vs changes in origin.
Both use rsync-style deltas to only send changes, but they use a content-addressable scheme like git so renames are a small metadata change record.
Also, both offer ftp and fuse interfaces if you need to access an older backup.