I'm not really happy with a lot of these changes. I guess I'll comment on the ones that stand out for me
You now control Cecil in battle in the opening sequence

Rydia has a new companion, the Pochika

Namingway has a new job as Mappingway (changing names appears to be unavailable due to voice acting)

Decant Ability System

Cecil cannot equip bows or staves

Arrows are not consumed when shooting a bow, and come in quantity of 1 from chests

Tellah is now able to earn sufficient MP above 90, with sufficient level ups. (thus allowing meteor to be cast early.)

New Hidden bosses

Kain and Palom are now right handed

Spell damage has increased for most spells

Bio damage reduced

Edge can no longer equip claws
That's going to be quite weird. They expect you to defeat a Zuu at the start of the game. I also doubt they'll give Cecil a free FireBomb...

I wonder what the Pochika does...

I actually like how you can't change names anymore. It'd only mess up the voice acting.

I don't really like the sound of the new ability system. They should've just enabled party member switching like in the GBA Version. It'll also ruin the "locked jobs" theme that FFIV is famous for.

They should've still allowed Cecil to equip bows and staves. That's what made him more unique than other fighters from other FFs. I know most people don't equip him with those but it is useful (using Artemis Bows on dragons doing insane damage, using the Sage's Staff to revive people).

The arrows, I'm somewhat okay with since Rydia fans will no longer be able to bash on Rosa saying that her bows and arrows are too expensive to be replacing all the time (seriously, liking one thing doesn't mean you have to hate on the other).

I'm not pleased with Tellah's MP being able to increase (they should've at least disabled Meteor from being cast).

I'm wondering where these new bosses will be...

They should've kept Kain and Palom left handed. It's not like it would be too hard for them to keep that.

Sure, they power up every spell except for Bio which they weaken (bye bye BennennaanaaaNAAWOU).

They also should've left Edge to be able to equip claws. That way you wouldn't have to throw them out after losing Yang.