I've used both over the years and here's what I've noticed:
Black - Black is nice with fish that are brightly colored and their surroundings don't affect their color. A marine Yellow Tang is a perfect example of a fish that looks fantastic against black. Certain colors also seem to 'pop' when on a black background; reds, oranges & yellows. It also happens to subdue certain colors such as blue, green & silver/grays. Obviously a black fish is going to look like hell against a black background

. With Peacock Bass such as monos and
kelberi, the gold and reds really seem to come out on a black background. As mentioned above,
Cichla such as
pinimia and especially
piquiti don't look as good against black. The bright blues that make these fish special tend to darken to the point that it's a non-factor. Keep in mind the tankmates/target/dither fish that will be in the tank as well. You don't want your Peas looking great and everything else blah. Lastly, for black to work well you really need to light the tank very well. You drop a nice Cichla in a tank with black gravel, black background and poor lighting and your display is going to be lacking. The key point here is to remember that fish tend to take on the "feeling" of their surroundings. A darker tank typically means a darker, subdued fish.
Blue - There are obviously numerous shades of blue. I'm not a fan of the light, powder blue that you see on many acrylic tanks. It is too light and tends to wash out the colors of the fish. Just as black darkens fish, light colors wash them out.
My favorite is a dark, royal blue. This gives you the benefit of darkening the tank like black does yet leaving it light enough that blue/green/gray/silver fish retain a lighter shade thereby showing off their magnificent colors.
Everyone has a personal preference but I find the dark blues the most forgiving and overall best match to a wide variety of fish.