Not a lot is going to change in Overwatch from now until launch.
Overwatch open beta content is what full game will have on launch
The currently ongoing Overwatch open beta is more or less indicative of the final version, in terms of content. Outside of some bug fixes, don't expect any drastic changes in the launch version.
That's according to game director Jeff Kaplan, who spoke on the official forums about the amount of content in the beta versus the full game. "The version you are playing now is what will go live at launch (there will be some bug fixes etc...)," he said.
"We're also working on a TON of post-launch features and content. It's going to be a pretty amazing summer."
Kaplan recently revealed that Competitive Play isn't available in the open beta because Blizzard is implementing the feedback the team received in the closed beta. Competitive Play also won't make it out at launch, but will be added "shortly after."