Two different questions hide in here: who points to me, and who points to my competitor. The first has an official, free answer; the second does not.
Your own site: Search Console
It is free, it is Google's and it shows what Google actually knows. In the links report you see the sites that point to you most, your most referenced pages and the text used in the links.
It is the most reliable source there is for your site, because it comes from whoever decides the ranking.
A competitor's site: a third-party tool
Search Console only shows your site. To look at another, you need a tool that maintains its own link index. The well-known ones have limited free tiers — usually enough to see a sample, enough to understand where a competitor's strength comes from.
What to look at, and it is not the number
Quantity misleads. Worth looking at:
- where they come from: sites in the same field or random ones?
- how many different domains: a hundred links from one site are worth less than ten links from ten sites;
- what text they use: natural variety or the same phrase repeated?
- how long they have existed: an old, stable link is worth more than a freshly created one.
What looking at competitors is for
To find out where you could be and are not. If three competitors appear in the same industry catalogue, that catalogue is an opportunity for you — and it probably accepts submissions.
Doing that for dozens of places is the work Magneth shortens, publishing your listing across the network in one go.
If your check turns up strange links, see bad backlinks.