One measure of competition in an industry is via Concentration Ratios. These generally take 2 forms:
In the U.S., these data are collected and measured by the Census Bureau's Economic Census (available every 5 years only); while some data releases from the 2017 Economic Census have been issued, the concentration ratio data won't be available until the establishment and firm size data by industry are released, organized by NAICS industry codes, currently scheduled to begin in November 2020.
1) The easiest way to find them is to go to Data.census.gov, and search for "concentration," then hit the button to View All Tables." That should pull up the most recent available tables, currently from the 2012 Economic Census. The tables are organized by major NAICS industry groupings, so you should be able to browse for the sector that contains your lower level industry. (Note: as you scroll down the results pane on the left, you may see a "Load More" button which you'll need to hit to see the full list). Open your desired industry to scroll through and explore the data. Hit the "Customize Table" to see a menu bar of options, including "Download."
Most industry grouping tables will show the n-firm (4,8, 20, and 50 largest firms) percentages of revenue earned; the Manufacturing tables show the share of "total value of shipments and receipts for services" instead, and also include the Herfindahl-Hirschman Index (HHI) figures for the 50 largest companies.
2) You can also use a shortcut if you know the specific industry code you want. For example, if you search: concentration 311111, you'll pull up a table with just that NAICS code.
Concentration ratio data from the 2017 Economic Census is currently scheduled for release starting in November 2020. | Release schedule
Tools used by economists and regulators to measure industry market concentration.
Two federal agencies have primary responsibility for antitrust law enforcement in the U.S. There are any number of entities that have jurisdiction in other countries. You may find economic analyses or legal filings on past or present mergers and acquisitions that shed some light on the competitive nature of individual industries.
The Census Bureau is one of the best sources for economic & demographic data.
In eStatement Studies you'll find Financial Ratio Benchmark (FRB) figures, broken down by US Region and revenue quartile, for a very large number of industries. Search or browse by NAICS industry codes.