DXT1 is for textures with no alpha channel. DXT5 allows alpha values. The difference between Reach and HiDef graphics profiles is that Reach requires the textures to be a power of two (POT) in width and height, but not necessarily square.
The texture compression selected by the content build pipeline is
* Desktop (Windows DirectX, DesktopGL): DXT1 for fully opaque textures, DXT5 for textures with alpha, specialized DXT3 for SpriteFont textures.
* iOS: PVR, with fallback to 16-bit (Bgr565 or Bgra4444) if the textures is NPOT (not power-of-two) and square.
* Android: ETC1 for fully opaque textures with fallback to Bgr565 for NPOT (due to PowerVR chipsets in some Android device), Bgra4444 for textures with alpha