Stop = VM will be shut down... so data in backup is 100% consistent under all circumstandes
Suspend = VM will be "freeze" for backup. So data can not change while backup is running..... but this can happen in the middle of a disk transaction.
Snapshot = Tell the Guest-OS via Agent to create a snapshot if QEMU-Agent available and then create a Snapshot for Backup. Also most often consistent.
To be slightly more specific: The VM will gracefully shut down so that it's in a clean state, then it will be started again with the vCPU paused, the backup process will set up tracking info for all devices and then unpause the vCPU so that the guest OS can start relatively quickly again.cause system/guest will shutdown and startup after backup.
As dirty-bitmaps are dropped when shutting down a VM, so slower incremental backups when using PBS, yes.
I personally use snapshot mode backups for running guests and backup jobs and stop mode backups in case of a maintainance task like before doing a major update or to migrate a guest to another host via backup+restore where downtime isn't a problem.
Or in other words: If I know I will do a restore later I use stop-mode backups. If I probably won't restore the backup and want it just in case something might go wrong, I use snapshot-mode backups as losing some unsaved data but having a recent backup is better than having a outdated stop-mode backup or no backup.