It’s much easier (and somewhat cheaper) to export oil than natural gas, so oil will probably be sold at a premium as long as the US is awash in natural gas. Oil is also a lot more convenient to use in transportation than natural gas.
Sounds like things are gearing up for exporting natural gas… Also, electric generation seems to be sucking up gas as fast as the supply can increase. The glut of a few years ago seems to have abated. Now, there is a glut of oil…at least for a while.
At the end of the day, a BTU is a BTU and the market will settle out based on who can use what most easily.