It seems the US is going to thrive with the former but naively stick our heads in the sands with the latter.
We’ll cede economic leadership, and wonder in 20 years what happened as other countries lead in energy. Even worse, the administrations stance will encourage US energy companies to pursue bad strategies, letting them avoid transforming their business. In 10-20 years they'll be bankrupt and the US will probably have to bail them out for strategic reasons.
The ice caps may be worse off for it, but there's little reason to think the USA will cease to "lead in energy" anytime soon.
If the rest of the world standardizes on solar+battery, demand for oil goes down, and so will the price. Which in turn makes US-produced oil not cost effective to extract, and domestic energy production collapses in favor of cheap foreign imports.
And then we're worse off in several different ways.
1) "We're out of easily extractable oil" maybe, but I've heard it before and technology does have a way of marching forward.
2) "Rest of world's oil demand will drop" is possible but certainly not happening today and far from certain.
3) "Then Oil prices will plummet in the US Domestic market" is far from a sure thing even if 2) comes to pass. How do the other producers - who don't have large domestic markets! - react? What happens to global petrochemical demand? And what sort of Industrial policy could shield our markets, even if this happens globally?
At the end of the day, we have a continent full of oil (and Uranium! which I prefer!) and an energy-hungry population.