As I said, you've got to play to their strengths. Obviously a Neifel Jarl is tougher for a toe to toe slug out, and if you play R'yleh like Neifelhiem it will be a total dud.
Don't do that. I've made the analogy before - Neflelhiem is a battleship, R'yleh is a submarine. Slugging things out toe to toe will be a dud every time. You've got to think more fade, dodge, and weave.
Here are some *significant* advantages EA R'yleh has to EA Neflehiem which you can use if you're clever.
1) Can recruit ready made thugs out of every castle, needing not a single item to take out most PD alone with a little research. Granted, you will need an amulet of the fish to attack the land, but strictly speaking they're effective out of the box.
2) All of the Mind Lords (capital only) and 25% of the aboleths (recruit anywhere) can teleport out of the box. This, combined with #1 means you can attack an absurd number of territories in a single turn against someone you don't even share a border with. Generally easy enough to forge crystal coins to get even more attackers.
3) As Meglobob mentioned, gateway is an excellent one-two punch to follow your initial teleportation wave with.
4) You can perform a brutal amount of mind hunting. This loses it's effectiveness late game, but can be stunningly effective midgame.
5) Most nations will be reluctant to attack you in the water early on. This is a powerful diplomatic tool as well as meaning you often don't need to sign NAPs, leaving you with lots of options once people start getting entangled in other affairs.
6) Voice of Tiamat + Dark Knowlege + Arcane Probing + Haurespex (+ Aschric Record for the land), R'yleh can quickly take a gem lead.