I have not been to any of the great art museums of the world but from what I have read the Portland Art Museum is not one of them. For Portland the Museum is a nice functional museum. They have gone for a wide collection and not depth. You can find samples of many styles and regions. Most with just a few items in each. It allows you to see samples from ancient Rome to some really strange contemporary modern art. I view it as good working museum for local artist. It is a place you can wonder through to draw inspiration or if you are looking at a design element that might have evolved across time and cultures.
The museum does try to find depth in its special temporary exhibit. These are only in for a short period. Sometimes these have a broader public appeal. If you are visiting Portland and not a regular art museum goer you should to check to see if there is a special exhibit going that might draw you in. I know when did the classic car design exhibit or the Sumeria Warrior armor exhibit those brought in a wide range of folks.