Quad core is a quad core, very true . Especially some modern games that scales good up to 4 cores.
For Embarrassingly Parallel tasks, 4 cores would likely be twice as fast as 2 cores. Video encoding is something close, compressing is close too. Other than these, getting near double performance is not expected.
By the way, quad-core running at 1.5GHz is almost never performance-equal to dual-core 3GHz. Really depends on what kind of tasks you're talking about. In some thread-hungry low-processing power cases (e.g. software graphics rendering, software physics, some matrix calculation stuff), email@example.comGHz can easily be faster than dual-core@3GHz, it works the other way round too, i.e. in some cases 2C@3GHz >> 4C@1.5GHz. Hyperthreading further complicates this.
And to end with, performance at 1.5GHz is normally not the half the performance at 3GHz, it doesn't work that way. It could be faster or slower, depending on the architecture (not sure about Skylake/Kaby Lake).