fins, do a little searching here for algae control. Lots of information has been presented about dealing with filamentous algae. It can be more complicated that Tom presented. First you have to determine which basic type of algae you have; planktontic (microscopic suspended) or fialmentous (cottony hairy masses). I assume that you are talking about filamentous. Most people commonly have filamentous algae problems.
There are some things in the old post topics that you can do to help prevent filamentous growths and ways to use less chemical to treat it. Example - explore barley straw and dye (shading) (i.e. search) as alternatives to chemcial herbicides for control of filamentous algae.
To get back to some answers to your questions. Copper sulfate (CuSO4) is quicker acting but more harmful to the pond ecosystem overall than Cutrine. Usually more CuSO4 is needed to treat algae than if Cutrine were used and since both have copper as active ingredient, CuSO4 applications result in more copper metal being deposited in the pond sediment/mud. Copper is a heavy metal and in the pond sediment it does not go away(deteriorate, decompose). Metals are stable in the environment.
Different species of fish have different sensitivities to the copper. Trout, Minnows, grass carp, koi are very sensitive to copper and small amounts will kill them. Whereas bass are fairly tolerant of copper ions and are last to die due to copper poisoning. Cutrine is "buffered" and not as toxic to fish as CuSO4. Alkalinity and total hardness of your water also has an affect on how toxic copper is to fish. Higher alkalinity levels equals less toxicity.
Typically label information requires the water to be 60F for best treatment results. However at 60F the bass and at 65F the bluegill start spawning. CuSO4 is pretty toxic to eggs & fry of bass and bluegill. Adults are less sensitive to active copper ions of CuSO4 than the smallest fish. Cutrine is safest to use if fish are spawning.
Lots more infornation can be learned if you do a search for algae control or Cutrine or copper sulfate.
In addition, Cutrine is available in liquid AND granular formulations. Each has benefits for use depending on the type of algae problem. Always spend a little time and read the label for instructions when using pond chemicals. GreenClean is a new granular algacide that does not contain copper and is supposed to be a safer product for treating algae. Search for that topic, it has also been discussed here, including words by a GreenClean representative.