I have a map layer of facility locations (points) in the Lambert Conformal Conic projection. I used the buffer tool to place a 3 mile buffer around each facility. I also have a layer of census block centroids that is in the same projection. I intersected the buffers with the census blocks to determine which blocks are within 3 mi of a facility. This worked fine. Next, I took the census blocks that are within 3 mi of a facility and projected from Lambert to UTM zone 10 (facilities are in Washington state). Within the UTM coordinate system, I see that some of the census blocks that were barely within the 3 mile buffer in Lambert are now just outside of it. For example, in Lambert one census block was 2.999 miles from the facility, but in UTM 10 it is 3.18 miles away. I know there differences in the projections and perhaps the datums, but this seems like a big error. Did I do something wrong? What kind of differences should I see between Lambert Conformal and UTM in the western part of the U.S.?
I would reproject everything into an equal area projection (Albers perhaps) and modify the standard parallels of the projection if necessary.