Should I use historical target-values versus the log with Amazon Forecast?

It usually depends on the data. Let's take a ordinary least squares (OLS) example. OLS regression assumes that the errors (residuals) are normally distributed. When they are positively skewed (long right tail) taking logs can sometimes help.

Also, sometimes the meaning of a change in a variable is represented better. For example, income. If you make $20,000 a year, a $5,000 raise is huge. If you make $200,000 a year, it is small. Taking logs reflects this:

log(20,000) = 9.90 log(25,000) = 10.12 log(200,000) = 12.20 log(205,000) = 12.23 

The difference between 10.12 and 9.90 is greater than 12.23 and 12.20