I think that depends on where you are moving from. IMO, no, there are no very bad areas of either town, even in the lower end of the housing budget arena. I just can't think of any ~
There are no longer remote areas of either town. Lake Oswego addresses range from Highway 43 to over by I-5; West Linn is a bit more spread out, being right on Highway 43 (aka Willamette Drive), the Willamette area of WL (aka Willamette Falls Drive), and the third part is up off of Salamo Road (where City Hall is).
That's a pretty rough sketch, but if you have access to Goggle Street View (such as putting in West Linn City Hall), you can get a taste of the surrounding areas.
Overall, I would have no concerns about either town. Some places are much nicer/safer than others, just depends on your needs and wants.
Keep posting and more folks will jump in with their ideas, as well. Good luck ~
