My favourite changes so far:
[dev1026] The system of claiming enemies has been overhauled.
No more complaints from party members when I killed other targets by accident, hahaha!
[dev1032] The following actions are now executable while in passive mode:
All magic spells
Actions which can be used on self or other party members
Now, that just really hyped me! Casting spells in passive mode? Totally awesome!!!
[dev1017] The Materia System has been implemented.
I can't wait to try that! New use for old equipment!
Inventory UI enhancements (equipped icon, spiritbond icon, etc.)
I wanted to say my thanks to the devs who thought of that, really useful.
[dev1176] The text command /battletarget (/bt) has been added which allows you to target the nearest enemy among those you are incurring enmity from.
Much easier to target and less targeting confusion while in party, yay!

The change I am not happy with:
HP and MP will automatically recover only while the player is stationary, regardless of whether or not he/she is engaged in battle. The amount of HP and MP recovered will increase based on the amount of time a player remains stationary.
Seriously, why????
This is really lame, really!

The things I will definitely miss and remain nostalgic of:
[dev1073] Physical level [...] has been abolished.
Other, unrelated to the above:
* Patch 1.20 will see accessories made repairable by NPCs.
Weren't accessories becoming like underwear, unbreakable?