In addition to @Behacad's helpful answer, here are some of many other points that could be made.
Your data include 8 factors, which I am going to call "predictors". Otherwise we might too easily get confused with the factors yielded by factor analysis.
My shortest answer is that your goal "to reduce the 8 factors [predictors] to a smaller set of variables" is not precise enough to say which method is better for you.
Beyond that, be aware that this is a large and contentious topic. There are statistically competent authors on PCA who would not want to get enmeshed in factor analysis and regard it as oversold. The standard monographs on PCA seem close to this position. Conversely, there are statistically competent authors on factor analysis who regard PCA as just a limiting special case of factor analysis that misses the main point of factor analysis, the scope for modelling the data. And because this is a contentious topic, many people would be unhappy with my summary.
But note that PCA would yield as many components as you have predictors. Reducing them to fewer could be your choice if you decided that you could dispense with the "least important", defined somehow. Alternatively, you could use the PCA results to choose a subset of the predictors. That could be done informally, e.g. by looking at the correlations between the predictors and the PCs. Alternatively, you could check out approaches such as that explained in
Cumming, J.A. & Wooff, D.A. 2007. Dimension reduction via principal variables. Computational Statistics & Data Analysis 52(1): 550-565
It seems simplest to me to regard PCA as a multivariate transformation procedure that maps predictors to PCs, with just one main decision, to base PCs on the correlation or the covariance matrix.
Factor analysis can be carried out in exploratory or confirmatory style, the latter being very much based on modelling, which should in turn be guided by your ideas about the data generating process. It is thus best to consider factor analysis as a family of modelling methods that requires you to make choices depending on your substantive hypotheses about your data.
Use of PCA analysis to select variables for a regression analysis