For analyzing backlinks of competitors my approach is to download the CSVs from Open Site Explorer for the top competitors (filtering for the entire domain and followed links).
Put these CSVs into an Excel workbook and convert each sheet into an Excel table (to make it easy to filter).
Sort the rows of each sheet by descending Page Authority.
Go through each sheet and highlight any URLs that catch your eye as potential link opportunities.
Lastly, filter the list to put the highlighted rows at the top so that you can look into these opportunities later.
The following Google query has worked well for me:
keyword phrase inurl:links