I find Elisif the only Jarl not corrupted by politics, she does care very deeply for the people. Her inexperience is what makes her great, she isn't like the others who are great liars. When I visited her for the first time she was going to dispatch an entire Legion to scour the hills and secure Dragonsbridge on pure speculation and superstition because one of those under her rule was worried. Her court advised her a more different approach is perhaps better since Nords are indeed very superstitious, but the gesture she portrayed was noted.
I don't think the strong in combat should always rule, there is more to strength than the strength of your arm. Great fighters don't make the best leaders. Some dislike her because they believe Tullius controls everything, Tullius isn't planning on staying in Skyrim forever, Legate Rikke is the only one who deals with the more political side after the civil war when she is put in charge of assisting the new Jarls. I much rather Legate Rikke than Galmar controlling half the Jarls of Skyrim.
I still don't see how many would see her as a Thalmor puppet, the Empire is certainly not a Thalmor puppet. Never met a puppet master seeking to destroy a puppet because the puppet is a threat. The only puppets I ever see are the Stormcloaks, completely unaware they're aiding the Thalmor plans, unaware they themselves are being given indirect Thalmor aid. The Empire are just pretending everything is all fine and dandy with the Thalmor, while they prepare for war.
"Most of the Legion is tied down on the border with the Aldmeri Dominion. The Emperor can't afford to risk weakening Cyrodiil's defenses. From the Imperial City, our war here is just a sideshow. An interlude before the main event against the Thalmor resumes." - General Tullius
Elisif is and will be a fine leader, certainly much better than Ulfric and his great plan to attack the Thalmor with no real idea of how to get there, with a bunch of magic hating people up against an all magic using army.
Axes vs the best archers in all of Tamriel, fireballs & lightning. Least the Legion employ battlemages. At least under Elisif's rule skyrim maintains more Nordic tradition, Ulfric's rule seems to disregard Nordic customs that date back to the first era so he can be High King. The Pact of Chieftains which certainly won't be of any use since Ulfric has Galmar to keep the Jarls in line, "Heh. Ulfric's put me in charge of keeping an eye on the new Jarls. You know, make sure they're generally following orders." - Galmar
So the real question comes down to, Rikke or Galmar.
"The General's put me in charge of assisting the new governments. I may understand things here in Skyrim better than the General, but I'm a soldier at heart, not a politician. But I'll do my best. This is the land of my birth, the land that shaped me. I'm proud to have any part in making it strong again." - Rikke
"Heh. Ulfric's put me in charge of keeping an eye on the new Jarls. You know, make sure they're generally following orders. Can't say I'm looking forward to that. But, I'll also be training men and women for their new armies. The Empire might send over a few Legionnaires to make sure we're serious, and of course, we'll be taking the fight to the elves soon enough. We'll need trained, disciplined and creative warriors ready for all that." - Galmar
Though under Ulfric's rule you can kill for a title then, going to see many High Kings and Jarls come and go. Don't want to pay your bounty? Kill the Jarl and become Jarl. Don't like the tax? Kill the King and become King. The Nord bandit's of Skyrim are going to love this. I think Tullius was right, without the Legion, Skyrim would fall into lawlessness and barbarism.
