It's gloomy and wet but it's a different sort of gloomy and wet. In Pittsburgh you get downpours and thunderstorms while Seattle is more of an endless haze for months at a time. In Pittsburgh an umbrella is useful while in Seattle it wouldn't make much of a difference.

Another big difference is that Pittsburgh in January will have its fair share of blue skies even if it's cold while in Seattle it's just grey from November until sometime in May. I first moved to Seattle in December and my wife never once saw Mount Rainer until late April or early May because it was always hidden by clouds. The summers, generally May into October, tend to have few clouds and mostly blue skies while the temperature hangs around a moderate 70°-ish for most of that (but with an occasional heat wave). Likewise the winter months tend to stay in the 30° area and rarely dip down low for extended periods.

Overall the total gloom between Pittsburgh and Seattle is similar but it's more sporadic in Pittsburgh and a bit bunched together in Seattle. Plus this is further exaggerated by Seattle being further north so those bright blue summer days last longer and those dark dreary winter days have even less day time light.