Google Analytics and Google Webmaster Tools (Search Console) give a wealth of information. If you set up Google Tag Manager, you can do so much more with what you're measuring. Top it all off and use the Google Data Studio to generate reports and you have a winning combination.
We do monitor some of our competitors but at a very limited scale as we interpret them that WE are their competition, not the other way around. To do this, that means that we need to put out the best information and provide the best service. Doing that will always mean that we are better than others. Yes it sounds cocky, but if you're not better than the competitor, why should a customer choose you in the first place?
As far as tracking what they do, we run a few spot checks on various key phrases that we may want to rank ahead on. We use custom programs that I've written to perform scrapes or scans, and then a few off the shelf programs like ahrefs, cora and screamingfrog. There are some other systems we use that I won't disclose here, but the rest is all manual interpretation and good ole brainpower.
