DXT3 only has 4-bit alpha, which means it's not good for gradients. You would mainly use DXT3 when it's either alpha, or not, basically just a well defined edge. But when you have a gradient like you have here then you need to use DXT5 since it gives you the full 8-bits of alpha.
If you had very fine control over your gradient then you could probably get away with using DXT3, but it's generally just too much work since you can simply move to DXT5 instead and not worry about it. DXT3 alpha should be a bit cleaner than DXT5 alpha would be (except for gradients obviously) so when you have rather sharp alpha transitions then going DXT3 might actually give you a little better quality.
Most of the time though, just use DXT1c if you don't need alpha, and DXT5 if you do need alpha. DXT3 would only be for special cases as far as FS2 effects and textures are concerned.
