Are there major advantages to InnoDB hot backup vs ZRM snapshots in terms of disruption to the running site, the size of compressed backup files, and speed of backup/restore on a medium-sized to largish all-InnoDB database? My understanding is that InnoDB's approach is more reliable, faster, does not cause a significant outage when running, etc.
If you want to avoid disruption to your site, the best method is to setup a replication slave to your server, and take backups from that. Using this, the method of backup becomes irrelevant, as the slave will simply catch up with the master when the replication is finished, and there will be no disruption to the operation of the master.
You can also setup your application to use the slave for read queries, to reduce load on the master.
I'm currently getting started with ZRM to backup a MySql server with only InnoDB tables. Based on what I've read, there should not be any disruption to your application at all using ZRM snapshots. It does not require a read lock for any amount of time.
I can't comment on size of compressed backup files or speed of backup/restore compared to InnoDB Hot Backup b/c I haven't used both products.
Also, if you register on the Zmanda Network you can download some good whitepapers. One of them is a benchmarking paper that shows speeds for backup/recover using InnoDB and LVM snapshots versus the other methods of backup that ZRM can do.