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I can not get 1km MODIS data aligned with ESRI basemaps in ArcGIS 10.2.2 for Desktop. See the photo below.

I reprojected MODIS17A3 data using the MRT (MODIS reprojection tool). I selected WGS84 under Projection Parameters. I tiled two files (shouldn't matter). My shapefile is in GCS_WGS_84 and it aligns perfectly over the islands. It seems that the MODIS data should move south and east. Generally, it is aligned, but there are some grid cells completely in the water.

I have several study areas in the Great Lakes region. Another is pictured at the bottom. Any ideas? These are quite north of the equator.

This image shows MODIS17A3 v.55 data over Apostle Islands National Park. The MODIS data are in black and white. The park boundary is in red. The basemap is the streaming layer in ArcGIS 10.2.2.

Sleeping Bear Dunes National Park

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A possible reason for the offset may be that the land mask of the MODIS data you use does not align quite well with your coastline shape file in WGS84 coordination system.

Another possible reason is that some parameters need to be adjusted when you translate MODIS' sphere to WGS84's ellipsoid.

Maybe you can try to convert the data to ArcGIS raster format without changing the projection and coordination system, then calculate the parameters yourself, and create a custom transformation in ArcGIS. This page provides some ideas and clues.

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