>But do you think that free software can keep up against these giants?

On an algorithmic front, definitely. The key areas where free software is kneecapped against large corporate interests are in marketing, which free software has never been good at, and in training set gathering.

In the case of the latter, google, facebook and microsoft have a major advantage in gathering data to do things like improve accent recognition, because they don't give a shit about collecting everything you say via services like cortana to improve their voice recognition, as long as it's legal. That technique applies to a whole suite of other problems as well, unfortunately.