It depends on how you mean better. In terms of power? Design? Used in the series?
The Sword of Omens is far more powerful and has a nicer design.
From a writing stand point though, the sword of power was never over used as a cheap and easy means to solve solutions.
We will have to disagree about that. I always found the sword of powers design rather dull.
I don’t recall the sword of power ever being able to fly and preform combat by itself so for the power sword to impale the eye of thundera might be difficult.
The Excalibur episode did show the Sword of Omens has that weak spot of the Eye of Thundarra, which the Power Sword does not. The Sword of Power draws from the Star Seed, the center of the universe, the Big Bang that created everything. It is literally all power.
If going by the earliest MotU canon, the Power Sword was basically just a key. In that regard, the Sword of Omens is far more versatile and powerful in application. However, being that the aforementioned key unlocks control of fortress in which is contained secrets that can make one essentially master of the universe, the effect of possessing the Power Sword would probably trump any ability the Sword of Omens can display.