Transformations are like drugs, some are good for you and some aren't. You should presume neither transformation but rather detect the appropriate solution based upon the data that you are trying to model. My answer to the log issue When (and why) should you take the log of a distribution (of numbers)?When (and why) should you take the log of a distribution (of numbers)? suggests that there is a logical procedure to determine to take logs or not. Taking logs or any other power transformation can remedy remedy non-constant error processes. Unnecessary/unneeded differencing of a time series can inject structure which then has to be taken out via model coefficients. Differencing is a form of an auto-regressive model and such should be identified as useful in separating signal from noise i.e. developing a useful ARIMA model. Outliers are not remedied by differencing this is accomplished by adding deterministic structure to an ARIMA model. See http://www.unc.edu/~jbhill/tsay.pdfthe which focuses on alternative schemes to deal with deterministic non-constant error process and the possible need for adding deterministic structure i.e. Pulses, Level Shifts, Seasonal Pulses and/or Local Time Trends.