Of the two Id probably take choose WA. UNLESS your thinking guided hunt then Oregon of the two.
If you was a tough hunt Cascades in Oregon have alot of good quality game and public land to hunt on. Elk, BlackTail, bear ect. Eastern Ore you better know someone or be wealthy. There are very vast tracts of land owned by Game preserves/hunting clubs. If you can afford to join one of them you can have great luck at good mature big game.
Its tough hunting but the top of Idaho has tags that non res can get into reasonable for DYI hunts and have great success for high quality big game.
Romey, not sure what part of Eastern Oregon your referring to but there's plenty of public land. I'd definitely not use that as a decider. Columbia basin Unit is mostly private but there are plenty of other units. I've never hunted Washington but my impression would be that Oregon's deer population is hurting more than Washington but Oregon is doing pretty fair in the elk department.
From Goldendale, you are probably closer to top hunting on the Washington side than Oregon but not all that closer. I think you are going to have to wait for someone who has lived in both states to weigh in. Awesome Sturgeon fishing to be had and i like Goldendale. I wouldn't mind living there.
For most part I am refering to both Biggs units (15% public)which do have alot of BLM but its almost all land locked by private and Maupin unit(8%) Grizzly(27%) A good chunk of Grizzly is R2 ranch, Fossil(14%) which is extremely limited. Yes there is some units with alot of public land and good luck drawing those tags. I know several people that cant drawin units they live in and go to Idaho to hunt. Im speaking for rifle hunting ofcourse.
I live in West Biggs. Last I heard it was 5% public, East Biggs, don't even consider it. The most public land around here is Grizzly unit and it get's hunted pretty heavy. Metolious has some decent area so I'm told and the Cascades has a lot of public land. From Goldendale or The Dalles your gonna have to travel some to find decent hunting in Oregon. It is there but private. Deschutes and John Day have some but not a lot and tuff hunting. John Day is accessable mostly by the river but most of that is past the falls so you'd have to go way around to do it.
When placing a trail camera don't just look for a well used trail. What you want to do is look for a freshly used trail off by itself that goes from a north facing ridge, thick forest, brushy knob or some other similar bedding area to a food source. Don't forget water sources. Especially in the summer months the deer need water so look for a good trail going down too a creek surrounded by thick cover and place the camera 100 yards up from the water source.
Scent control is very important...