What system should i back up ? system_image or system I am trying to backup my system but i have two partitions, system_image and system.. from inspection i can see that system_image is bigger and the format is ext4, While system is smaller and the format is emmc ..    

I may have the formats (emmc,ext4) in the wrong order.  

What do i back up, system or  system_image  ?

I also have system modifications that I'd like to keep in the backup.

Device :
Android 5.1
this concerns TWRP only and is just a different method for backup &amp; restore  

have a look in /etc/recovery.fstab
you will see the same partition is listed twice  

/system        ext4  /dev/block/bootdevice/by-name/system  flags=slotselect
/system_image  emmc  /dev/block/bootdevice/by-name/system  flags=slotselect


first entry is listed as ext4 file system type which tell TWRP the partition is mountable. in case of backup / restore only the content (files) are archived into system.ext4.win (tarball archive)  

second entry is listed as emmc which makes TWRP think it is raw disk image. in case of backup / restore the whole partition (including empty space) is cloned bitwise into full partition image system.emmc.win (dd image)  

usually /system is sufficient for backup purposes.
/system_image is useful for restoring foreign ROM or backup of corrupt data  

Note: for system-as-root devices the mount point is changed into /system_root while /system is just a symlink (or bind mount) of /system_root/system (which is not a representative of whole partition)