Having played both games, I can safely say no, they aren't. They are similar, but in the same way that Metroid Prime and Call of Duty are similar (here's a hint: they aren't really). Allow me to explain why, and to do that I will start by talking about what Battleborn is:
Battleborn is the team-based arena shooter developed by Gearbox that released on PC, PS4, and XB1 not too long ago.It advertises itself as being a badass game filled with badass heroes for badass players and just really REALLY loves that word "badass". But then again, these are the same developers who brought us Borderlands, so that's not too difficult to comprehend. In practice, Battleborn is a first-person arena shooter that uses MOBA elements to create a unique and cartoony multiplayer experience, as well as a Borderlands-style story mode. Each of the games current 25 heroes is completely unique, has their own skill set, and a colorful array of dialogue. The game uses comedy to great effect in order to make the game feel like it doesn't take itself seriously and therefore neither should the player. Normally I would say this is a bad thing for a competitive shooter but Battleborn manages to do it in a way that comes off as "look bro, we're just here to have fun. Don't be toxic to your team, don't worry so much about winning, just get the hell out there and blow shit up". The game's painted landscapes and colorful visuals, as well as intentional censor bleeping of swear words makes it come off as a cross between a television show and a video game, which is true to the standard Borderlands design that is to be expected from Gearbox.
As for actual gameplay, it's a lot like a MOBA: each character is pre-made with their own theme, personality, and set of 4 skills and a passive, as well as augments you can get as you level up in a match to alter their abilities to suit the situation or your own playstyle. There are 3 pvp modes: a 1-lane + jungle MOBA map where you push minion waves and capture objectives to destroy the enemy teams sentry robots, of which their are two. But instead of lasting as long as it takes somebody to win, each match has a maximum of 30 minutes. If the timer runs out the match either ends in a draw or the team who has the highest total percentage of sentry health (each sentry accounts for 50 points for a total of 100) wins. There is also a traditional 3-point king of the hill mode, as well as a minion-pushing mode where the goal is to push your minions to the enemy teams altars and sacrifice them, with each minion sacrificed giving you points depending on how big it is, with the first team to reach the goal or whoever has the most points at the end of the timer winning the match.
The solo campaign follows traditional Halo-style "point A to point B with enemies and objectives between you" linear maps with the story about how an evil interdimensional force is destroying all the stars in the universe and a coalition of several factions populated by the last living races in the universe fighting to prevent the last star in existence from being destroyed as well. Cliche, but imaginative. All in all it's a solid, fun, goofy shooter meant for MOBA players who like Shooters as well.
As for Blizzard's latest addition to the Battle.net launcher, Overwatch is still a team-based arena shooter but the way it approaches things is a lot more akin to Halo multiplayer or Quake than a MOBA. Matches are attack/defense/payload (as far as the Beta has shown) on asymmetrical maps filled with twists and turns and buildings and all sorts of other potential avenues for tactical advancement. Each hero is, like Battleborn, given their own unique theme, personality, dialogue, and skillset. Each hero has a basic attack with their primary weapon, two utility skills, and an ultimate which charges over time passively and by damaging and killing enemies. The time-to-kill in Overwatch is tiny, with many heroes possessing ultimates that can easily wipe out the entire enemy team if positioned properly. The balance to this is that respawn times are very short and do not get longer. They are essentially as long as it takes you to watch the kill-cam of how you died which is a fixed length of several seconds, and then you are back in the game. The atmosphere of the game is still colorful and full of life and action, but the mood of the game is a lot more serious than Battleborn. Overwatch has the air of a comic book, while Battleborn has the air of a late-night comedy show. I only played the Open Beta for a few days, so I can't give too much else about Overwatch, but I liked it enough that I did preorder it and look forward to playing it on the 24th, and so will give a much more detailed overview of the game when I get my hands on the full version.
To summarize:
Battleborn is a shooter for people who like League of Legends and shows aired by Adult Swim.
Overwatch is a shooter for people who like Team Fortress 2 and Marvel movies.
You can buy Battleborn from Steam here for $59.99:
http://store.steampowered.com/app/394230/
You can pre-order Overwatch from Blizzard here for $39.99:
https://playoverwatch.com/en-us/buy/
