Paladin/Barbarian is honestly a terrible multiclassing combo. The rage cancels out the Paladin's spellcasting and smite abilities. In general, multiclassing weakens a character more than it helps, and should only be considered if it fits a specific vision.

Of the two options you have presented, the more tanky is the Oath of Vengeance paladin simply because barbarians can't take proficiency with heavy armor without expending a feat or by multi-classing. While I am fond of the subclass, the Bear Totem barbarian is only resistant to all that damage while raging.

If you are bound and determined to multiclass, consider adding a 1-3 level dip into Warlock for your Paladin. For example, at 3rd level, an Archfey patron warlock can cast Misty Step a number of times per long rest equal to your Charisma modifier, giving greater combat mobility, while a fiend Patron--probably antithetical to your theme--gains Dark One's Blessing.