Sometimes you can beat free! You can outlive the free / freeware competitors, because they're often not making money!
Remember Google often kills off their services. They bought Picasa & the Nik Photography Collection & made them both available for free... now Picasa is gone (even though there's a ton of customers who still want it), and Google sold the Nik Collection to DxO and it's back to costing $70 again. And Fastmail exists even though Gmail is free.
Google is not known for providing friendly personal customer service... so why not aim to get your customers saying "yeah XYZ costs more, but oh my god, they have the friendliest & most hilarious people answering their emails, and they actually fixed my problem!" You can only do that if you've got money coming in to pay for the support team (you want to pay your employees well too, right?) Derek Sivers has some great ideas on doing awesome customer service:
(Anyway, just some food for thought. Sometimes pricing cheap is absolutely the right thing, sometimes Charge More is the right thing. Experiment with both!)
I said on price. Beating service on stability and support is not competing on price - that is very much possible. You can compete with Google on both of you aim at their enterprise package or cloud offering.
You can compete on price. But definitely depends on your niche and market segment though.
There are plenty of users who are not happy with how the big companies create products. Google and Apple create for the mass market and in the process generally eschew features, functionality and quality of life improvements which a certain subset of users demand. That's why people pay for Evernote, Todoist etc even though Google/Apple notes and reminders exist. Some companies have even raised VC funding for creating calendar apps even when Google calendar exists.
If your potential customer is happy with the free product, then they were potentially never your customer in the first place. Creating product in such a niche won't be easy nor will it make you a billionaire. But there's a decent chunk of money to be made in both B2B and B2C.