Neolibs and neocons are both pro-welfare state pro-mob rule pro-degeneracy.
I don't agree with your premise, but what you're saying about two sides of the same coin is mostly entirely true.
Although Neoliberals and Neoconservatives aren't at all diametrically opposed.
Neoconservatism is a foreign policy based on spreading your own ideology through war, and it's a term only used in America.
Neoliberalism is an economic policy based on deregulation, somewhat progressive tax rates (usually top bracket is 40%), service-based economies, some privatisation, yet by-and-large retaining the welfare state. It's a global policy
Because of this, some people adopt both policies, like Reagan or Blair. it transcends the political spectrum absolutely- leftists and rightists have both been infected since Reagan+Thatcher, and Clinton+Blair. Thankfully Sanders/Trump/Corbyn/Farage are trying to put an end to it, but Trump in particular looks to be fickle af, sadly.