I want to know who you think would be the best Jarl to rule for each of the holds e.g., Ulfric VS Brunwulf in Windhelm, Balgruuf VS Vignar in Whiterun and so on. Please share your reasons behind your choices!

I like Balgruuf, most of the Jarls are either incompetent, inexperience, lazy, corrupt or just unfit to rule. Maybe like Brina, Vignar, Idgrod Ravencrone, Brunwulf and Kraldar, they don't seem corrupt or incompetent.

Otherwise the rest I look down on as unfit to rule. Though I think Dengeir is probably a decent jarl and is right to be paranoid of spies that paranoia hurts him a lot as it will stop him from fully trusting people, Laila is nothing but a puppet who doesn't know she is one, Maven makes regular use of the thieves guild and hires the dark brotherhood, Silver-bloods are oppressive as hell, Igmund is a puppet of the silver-bloods, Korir is a sad sack that doesn't even try to rebuild winterhold he just drinks and blames the College instead of using the college as a way of rebuilding the hold, siddgeir is lazy, Skald is a moron who dismisses the dragons as Talos being angry and not to worry about it, Sorli is in it for the power she even mentions she wants to end up ruling Riften, Elisif is inexperience and still grieving though she is young so she could probably learn how to be a decent leader if she gets someone to teach her, and I think Ulfric is all talk and hasn't shown himself to be a good ruler at all but I'll probably get all the hate for saying that.

Vignar talks about rebuilding the hold and he has friends in the companions, he probably knows a thing or two about honor.
Brina talks about fortifying the hold and actually sees the dragons as a threat unlike Skald
Idgrod seems fine with what she has
Brunwulf talks about improving the hold for EVERYONE and is making plans to work on that, he isn't ignoring or segregating a race from the city
Kraldar realizes that the college isn't something to shun, he can probably rebuild winterhold with the help of the college
Balgruuf cares about his people, he sent troops to Riverwood without caring if it could end up with falkreath taking it as an act of war.

One of the only decent Storncloak supporting Jarls is in Riften. Otherwise most the other cases I tend to favor the Imperialist Jarls.

The Stormcloak Jarls seem a lot more traditional (Nord-wise) in their outlook and ways and it come across in the way they speak to you. Which comes across much more abrupt and less diplomatic.

That saying, it is the Nord strong will and lack of being swayed to others opinions that has possibly helped them be so victorious in war. They have strong self belief they are right.