I think being able to save anywhere makes the game a lot easier. The thing that made Ice Cave so hard in NES/WSC/PSX was that enemies might ambush you and annihilate your party, forcing you to restart the dungeon. You no longer have to restart the dungeon if you keep saving all the time in the dungeon. Now you don't have to buy a Sleeping Bag or go to an Inn every time you want to save the game, either. I liked FFIVA's system where you can save in the world map and save points, and create a temporary quick save if you ever have to quit playing in the middle of a dungeon.
I played FF1 DoS yesterday, continuing with my party of Red Mage, Thief, White Mage, Black Mage. Their leveling up speed is huge, I think they were on level 16-17 when I went to the Marsh Cave. o_O Buying spells for three mages is quite expensive, but since the spells are cheaper now, even that is possible. My Black Mage has almost 200 MP, and both Fira and Thundara take 15 MP, so he could cast them in almost every "tough" battle in Marsh Cave (read: jellies or a large group of enemies).
With their newly added extra hits, this team was able to defeat four Hill Gigases in the peninsula NE of Pravoka on level 15. Haste + Temper + Protect (or Invisible) = battle won. The fact that you can buy Phoenix Downs and some status-healing items not present in NES, and that enemies can drop some very good items, will make things even easier. I got an Ice Shield from the enemies in the peninsula NE of Pravoka, though I don't have a Fighter/Knight or a Red Wizard, so I can't use it yet.
In short, FF1 DoS has so far been very easy.