So I've been transitioning to GURPS lately.

For smooth, simple gameplay you can run GURPS Lite. Or Ultra Lite, I don't think it's possible to get much simpler than Ultra Lite.

However, there is also a lot of content in the full system and supplements, so you can add the bits and pieces you like to the Lite framework. Want modifiers for targeting specific body areas? It's in there. Want penalties from bleeding out? It's in there. Want a robust magic system? There are several to choose from. Want to homebrew abilities, items, spells, pretty much anything, without breaking the game balance? All the tools are there.

Everything is customizable. It's designed for any setting. Sure, there are a lot of rules, but even the publishers are very insistent that they're all optional. It's basically an encyclopedia of mechanics you can use to add as much crunch as you want to your game of make believe, whatever that looks like.

I have been where you are (although I left DnD at 4e).

I ended up switching to Savage Worlds. For me it hits the sweet spot of crunch and narrative freedom. The combat is grid based like DnD (or Theater of the mind if you prefer), but even max level characters don't take more than a minute or 2 to resolve their turn. It's dead simple to learn well enough to run and play but offers a great variety of more in depth mechanics if you want to spice things up. (IMHO it has the best system for mass battles of any published system and one of the best chase mechanics, two things that are severely lacking in e.g. DnD).

As for settings:

• Pathfinder has a really good official Savage Worlds version, if you want to stick to phantasy
• Deadlands (Horror Western) is phantastic
• 50 fathoms is pirates
• Rippers for Van Helsing Style monster slaying
• Big Apple Sewer Samurai: Teenage Mutant Ninja Turtles without the official license
• Homebrew settings that I've run: Stone Age Super Heroes, Avatar the last Airbender meets Roman Legions behind the Steampunk Stargate, Firefly

I think you can cross of PbtA off the list, since it is an engine rather than a universal rpg. You surely can run any setting in opbta but you'd have to write the according Moves from scratch.

Cortex Prime is a toolbox to build your preferred level of crunch and/or focus driven system, so there is a lot to put together before you even get to setting specific stuff.

I liked running Genesys but my players did not. We are all pretty happy with Savage Worlds right now and imo it checks every box you have mentioned.

Genesys is kinda good. My preferred generic system. Enough crunch and customization to give it meat while still flowing nicely. Only downside would be if you and your group needs physical dice as it uses proprietary ones.

Ironsworn (especially with Starforged) can almost be used as a setting generic system. Change up Oracles and Assets and you have a whole new setting.

You can also look at families of games, such as Crawford's X without Numbers. There you will get a system made for a setting but it still being oretty much the same system.

Of the systems you listed, and based on your requirements, I would suggest looking more into pbta/dungeon world, old school essentials, world without numbers, and maybe black hack. Though a number of them I have far from any amount of experience with, so there might be better ones listed too.

You might also consider Index Card RPG

PbtA is more of an engine than a game. You can technically run anything with it if you don't mind making entire play books for each setting. At that point you're basically making a new game

I'd recommend taking a look at BESM though. It's more anime themed, but it's a competent system with a lot of flexibility built in. Magic kinda has rules, but it's treated like any other power your character can have. You buy the effects and limitations of your spells when you make or improve your characters

Another good option is WOIN. Technically it's 3 games (OLD, NEW, and NOW), but all three books are fully compatible with each other by design and the medieval fantasy book (OLD) has rules for magic and creating a spellcaster. The 80s action movie book (NOW) has rules for firearms and mutant powers, and the space faring sci-fi book (NEW) has rules for cybernetics and psychic powers

From the games you mentioned, the most flexible ones (that I've actually read) are: Risus, Fate (same as fudge), Savage Worlds, Whitehack, Freeform Universal, Hero System, and Worlds Without Number (mostly compatible with Stars Without Number btw). Of those, the fastest combat is probably Freeform Universal. Savage Worlds is fairly fast too, but more tactical. Worlds Without Number probably has the most consistent combat pacing though

I really like Fate. It's a generic system you can run in any setting. It doesn't have any of D&D's stupid baggage like martial-caster divide or the adventuring day. The way aspects work feels to me more intuitive and like how new players try to do RPGs. That's stuff like "But he's a paladin surely if I invoke his love of justice he'll go along with our plan." New players try that all the time until D&D hammers the idea out of them.

However! Fate does not really work if your players suck. Sorry. Passive players that want to just sit there while you tell them a story aren't a good fit. Players that get easily discouraged and give up rather than coming up with clever ways to succeed-with-cost won't like it. It's described as a more writer's room mode of playing sometimes. Everyone needs to have a little GM in them. But then it can be a lot of fun.

Thank you very much for your replies! After some more research based on what you've told me, I'll settle with Worlds Without Number and keep Genesys and Mini Six as back-up plans.

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