The remake is easier to play through, but some things were fixed/changed that make it 'harder' to become powerful faster. Being able to hit another badguy helps (but don't spells still 'miss'?), but you can no longer get as much money as you want from the Thunder Staff so you have to actually fight around to get the better equipment (I know a good place though), and you can only get 1 Water Cloth in the remake. The 2nd prince can also equip the Loto/Erdrick's Sword in the remake.
Then again if you got the Gold Card, it may not be hard to get a bunch of Mage Staves or Prayer Rings to get money anyway.
They added seeds to the game, but they don't help too much. Sleep is pretty effective (may be too effective) but the overall difficulty of the game was toned down. It still can be darn tough, though. It just seems more forgiving and a little better balanced for most of the game, to me anyway. They may have increased the experience some monsters give out (they certainly did for Metal Slimes in both games and the little puddles in DQ2) in DQ2 while in 1 almost every badguy gives more experience and/or gold. They're both quite short compared to the originals (I've gone through them both in one sitting, something I'd not be able to do in the originals).
Have fun! Oh, I was comparing the GBC/SFAM ones in my earlier post. They aren't very different. The originals are, though. You can rename the alternate party members in the GBC/SFAM version if you want, bluemax.