Upshot may have two meanings: 1) consequence, conclusion 2) summary, bottom line In this sense it's closer to outcome in the first sense mentioned above. I'd say outcome has a more positive feeling to it than upshot, which could be either way.

"Upshot" has the implication of an unintended outcome or consequence, or a secondary one {or side effect}. For example, an upshot to finding eternal life could be that you became a zombie. :D Edited: By the way, this could be used conversely also. Ex: The upshot to the economic recession/downturn is that now, mortgage rates have fallen and housing is more affordable.

Upshot is usually used to indicate something good that happens because of something else. English use does not specify that it has to be good, it just seems to be more common. The two words are actually synonyms. The outcome is what happens and does not ever imply that it is good or bad. What was the outcome of your job interview? What was the outcome of the 100m race?