Since you've asked, I would (obviously) choose 3'-seq ;-)

But why stop at inquiring about those two? (It would help if you provided references to the protocols you are talking about, as it's not quite clear which protocols you are referring to, by name)

There are many more sequencing protocols that were developed over the last few years that generate the same type of data (i.e., tagging and sequencing only the terminal ~ 100bp of a transcript and junking the rest). This was largely because most of us were working on the analysis of ApA when there was no protocols (aside from "normal" RNA-seq) that would enable you to do so at high resolution and in a high throughput manner, so different labs decided to take matters into their own hands and were developing these methods more-or-less concurrently -- which then resulted in a slow (or fast, depending on whether or not your study had been published yet ;-) train of papers that came out, each with their own methods to do the same.

I don't think you'll find a satisfying answer for which method you should choose -- I'd recommend trying a few different methods on a cell line you have some "ground truth" data for, and use the method that gets you close enough to what you think you already know.

Some of the methods that came out around 2013 or 2014 (Bin Tian's, in particular) also included a step that purported to mitigate the effects of internal priming, and thereby reducing the number of false positive cleavage sites from the bench, whereas many (including ours) requires you do some sequence analysis from the data after alignment in order to remove false positive peaks purely in silico.

This is the protocol I'm thinking of (I've never tried it myself):

Accurate Mapping of Cleavage and Polyadenylation Sites by 3' Region Extraction and Deep Sequencing