What are some publicly available tools that provide metrics on competition? Can these data be used on a pitch deck or mentioned when pitching?

Alexa is probably the worst tool you could use specially if you are trying to gauge international traffic. Try something more advanced like similarweb.com to measure traffic volume and geo breakdown. Appannie.com will help you to analyze apps on itunes and google playstore.

I would include the source always. Crunchbase, wikipedia is always a good source but be aware. Slideshare is a great tool for this. Always cite source.

Depending on the sector, there will be free reports available from various consulting companies analyzing the various opportunities.
This is an excellent data which can be actionable as you are basing your projections on the widely acknowledged data by investors and on a good research done by a firm specializing in the industry in which you want to enter.
By making your case based on these reports makes your pitch stronger and you come across as a person who has done your primary research well to your investor.
If you want to check up some specific examples on how to use these, I am glad to go over in detail over a call.

When I go through the process of building a competition slide for a pitch deck I like to include several "forms" or competition.

1. Monopolistic Competition: Big players in your space, these are the Microsofts, Oracles, Google's of the world.

Tools to use: Public companies announce quarterly earnings. Understand where their revenue is coming from and what's growing the fastest. ex. http://www.sec.gov/Archives/edgar/data/1288776/000128877614000075/goog10-qq32014.htm#sE456F21B4F58076BCE0E8E07A40E64F4
It's also worth reading into what financial analysts say about each quarterly earning report. They are normally small picture thinkers but they almost always focus in on what the company is spending most of it's growth efforts on.

2. Distribution Competition: These are companies that will be fighting for the same distribution channels and advertising channels as you.

Tools to use: If yours is a mobile app, the best tools is App Annie, look at apps that compete in your category. You will have to fight these apps on download volumes and ratings even if they don't directly compete.
http://www.appannie.com/apps/ios/top/united-states/social-networking/?device=iphone

3. Audience Match Competition: These are companies that target a similar demographic profile to yours. Similar to distribution matching, these competing companies will be fighting for the same ad dollars.

Tools to use: Some of these are dated but it is a good list: https://blog.kissmetrics.com/25-sneaky-online-tools/

4. Use Case competition: These companies have a similar use case or have a solution to your problem (even if the solution is different)

This could be as simple as you're a note taking app and a use case match cold be a notebook, they are still worth brining into the slide as they inflate your solution as the obvious better solution.

Google Adwords and similar CPC platforms will allow you to research search volumes for particular phrases as well as advertiser bid competition and cost per click.

These data can be indicators of both

(1) audience interest / consumer demand

and

(2) niche competition when it comes to customer acquisition and lead generation online.

Depending on your objectives, referencing such numbers might be highly relevant for pitching or not. But understanding these metrics is crucial for any business that plans on being found online.

If you have any questions about what I've mentioned, let me know.

All of those are great suggestions. I'd like to add www.Similarweb.com, as well.

You may use these data in pitching but remember pitching your start-up idea or product to a room full of investors is extremely nerve-wracking. With the right presentation deck, you can hold potential investors' attention long enough to explain what your product does and why it is a good investment. A good presentation is not a substitute for a good product. The two main issues that top the list are an unviable business model and only plain old running out of money. Your goal here is to create a very high-level overview of your product or service. Do not put too much text on the slide. You want to hook the investors right away by speaking about your product. I would suggest creating one impactful statement that sums up your product and having that be your overview slide.
A few notable tools that can help you are as follows:
1. Crayon: It combines both human and artificial intelligence to provide insights that enable your core sales, marketing, and product team to device strategies that succeed. Everything from a pricing change to marketing campaigns by your competitors is consistently monitored and assessed by the tool.
2. SEMrush Traffic Analytics: SEMrush Traffic Analytics is a must tool for competitor research. You can learn what keywords your competitors are ranking for, whether the ranking is organic or paid, and how much are they paying to rank.
3. SpyFu: SpyFu is widely popular among the digital circles as a substantial SEO tracking and monitoring tool. Kombat tells you how your top keywords are performing as compared to your competitor’s keywords. SpyFu also comes with an innovative dashboard that handles all of your essential metrics which include monthly clicks, cost per click, and click-through rate.
4. Moat: Thankfully, Moat is just the tool to help you with that. This information can prove to be a huge boon for your company to create creative content inspired by your competitor’s old work. It allows you to travel up to three years in the past to review your competitor’s campaign ads. Moat is like a muse to your business’s creative team. It inspires them to create winning creative content that has the power to engage your audience. Moat puts audience engagement front and centre and paves a path for you to achieve it.
5. Owletter: Best for monitoring competitor’s performance, Small and Medium enterprises. It offers users a competitor analytics feature to know what your competitors are doing. By learning about your competitor’s email strategy, you can learn of opportunities in which you can send your emails.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath