It was heavily inspired by roguelikes, the game was even turnbased early in development.
Belzebub is pretty good, though mind that it adds a lot of new content, new dungeons, new functions, just lots of new stuff.
It also always generates the side quests, unlike the original game, where the game kind of just rolled a bunch when you started, and as you played you would just gradually find out which quests were there, and which weren't.
I guess this was to make sure that there were surprises and new things for a player, like "Woah, 'Chamber Of Bone?' That's a new one!"
If you're a guy like me, however, it's a nice change of pace because you don't have to 'reroll' the dungeon to get the quests you want.
Another change is that in the original, you can save and load the game as you please, however Belzebub does it different, it just saves your progress automatically, as you go (not sure exactly how, maybe between cell transitions), and when you die, it's not just a game over; load last save, it instead respawns you in town, with all your stuff, and full health. The situation you died to is still down there, and you can go down there and find them, at least on normal mode, you get no direct penalty for being killed.
The ability to carry a spare weapon set equipped on your character is a feature from Diablo 2: Lord Of Destruction, and frankly, this feature is a very nice one to have, it lets you be much more flexible in tactics, you could carry a bow or an axe as a secondary weapon (perhaps with specific damage types or abilities), for different situations, or maybe a staff. Gold also stacks higher.
The original game is still great fun, but it's not always so smooth to run on modern PCs, and I've played it in and out since I was a little boy in the 90's, so a lot of what Belzebub does breathes some new life into the game and gives a lot of new content.
A lot of the new things are leftover beta content, which Hellfire also did, but Belzebub does it a LOT better.