As nobody has responded, I wanted to add my own piece.
I'm familiar with both techniques and know that they are similar in the sense that they both principally aim to target DNase I hypersensitive sites (although FAIRE can be used for other markers). That said, I don't know the exact differences in pull-down methods in both techniques, and whether, for example, read coverage or region size (covered by reads) would differ between both. In that sense, I would advise not to use
-style dnase for your FAIRE data.
Sure enough, I have just done some searching and it is even recommended on the HOMER website to not use
-style dnase for FAIRE.
Two Different Types of DNase-Seq (Important!)
So far, there have been
two heavily used protocols for DNase-Seq. The original method from
the Crawford lab first ligates an adapter to the end of DNase-cleaved
DNA fragments, and then sequencing into the fragment, often creating a
"tag" in the process. The 2nd method involves extracting
DNase-treated DNA and then size selecting for fragments of size
~50-100 bp. In the 2nd case, the idea is that open chromatin regions
are likely to generate DNase cleavage sites less than 100 bp apart
(creating a sub-100 bp fragment of DNA, say on either side of a
transcription factor binding site), while nucleosomal DNA will likely
produce fragments >150 bp (the size of a nucleosome). The first
method is more faithful to the recovery of DNase cleavage sites, but
the 2nd method shows very robust enrichment at regulatory elements and
looks "cleaner". That comes with the catch that the 'open' regulatory
element must be of a certain size range and capable of generating
cleavage sites in the right size range. I'll refer to these as the
"crawford method" and "size-selection method" to keep them straight.
Why is this important? The original Crawford method measures DNase
cleavage sites (and the strand information is less important), while
the size-selection method is a lot like ChIP-Seq where the regulatory
element with transcription factor binding sites is likely to be on the
fragment of DNA extracted in the size selection process. In fact,
DNase-Seq generated with the size-selection method should be treated
exactly the same way in HOMER as ChIP-Seq data.
If you want me to summarise this for you: the HOMER author refers to the 'Crawford method' (original DNase-seq) and the 'size-selection method' (FAIRE-seq). The author relates exactly what I stated in my response (above), i.e., the pull-down method is different and thus region size covered by reads.
The source page to which I linked goes through the tutorial for analysing both.