i think i played at least one full campaign with each of them (though some of that was in FE, so the rules have changed quite a bit and they may be a bit different now)
that's a really tough decision. Pariden is definitely among my favorites, but i also enjoy Capitar and Kraxis a lot. Gilden and Yithril aren't too bad either, though a bit one dimensional.
EDIT: totally skipped the "and why?" part of the question
Pariden is great because all their abilities work together - scrying pools give you more mana when you need it, Monoliths allow you to expand influence quickly and grab shards and the shards power up the stats of your troops and also improve many spells in the multiple spellbooks you can have on every hero. their default sovereign, Procipinee, starts with the 3 (IMO) best spell early game spell schools and she can be tweaked to be a summoner, a great support spellcaster (heal/buff/beduff) or a damage specced evoker (storm & blizzard are pretty solid; and you can always just slap on Annointed by Fire or buy a fire epllbook later if you want to go that toute).
very nice setup IMO.
capitar is not as nice, but the +1 move and road building make their units very mobile, the accuracy buff gives them a nice damage boost, their orsesa re a bit better than default and their sovereign is probably the best trait combination you could come up with for an epic commander. he can grab battle cry at level 5, then pick up life and air spells to complement his arsenal (heal/AoE heal/growth/haste/titans breath/cloudwalk/tornado/guardian wind - all of them are great utility skills for a commander)
Kraxis is a bit odd. actually i mostly like their troops (spear&shield + the tactical fortifications and the krax blood make them very tough to beat, even with crappy early tech items). their sov isn't that great. wealthy is nice and water is a nice early on, fire is more usefaul later on. can be a pretty decent damage caster if specced for it (fireball, flamedart & blizzard). never got much use for the whole Betrayer faction trait or the silver tongue sov ability, though.
Gilden and Yithril are easy to understand and don't offer a lot of finesse, but their traits are solid and support what they are doing. Gilden is all about having impenetrable high armor units and Yithril is all about brining the pain with their super axes wielded by super soldiers.
to be honest, i think i like all of the premade factions. if you think about the traits a bit and form a strategy around their abilites, they can all work out nicely.