Does Obsidian deserve to work on another Fallout game? Bethesda gave them the short end of the stick last time. They paid Obsidian a flat rate, so even if it sold 35,000,000 copies, Obsidian wouldn't be any richer if it just sold 200,000. Since new Vegas got an 84/85 on metacritic instead of 85, they didn't get a bonus that was part of their agreement. While you could say that they don't deserve their bonus because they were off by 1 point, that one point was easily caused by Bethesda themselves because they handed Obsidian a faulty engine and they knew it. Morrowind, Oblivion and Fallout 3 were both incredibly buggy games, so New Vegas would be as well. So it looks like they were set up for failure. One of the main criticisms of New Vegas is the bugs, which are unavoidable with Gamebryo. Hell, when Skyrim was going through serious PS3 memory issues, it was an Obsidian dev who commented as to why that was happening, so Obsidian does know what's going on. Plus. Beth did the majority of not all the QA for New Vegas. I think Beth also wanted New Vegas out for a while and done with DLC wise before Skyrim would hit, because they don't want competing.
While nobody is worthy of creating a Fallout besides Obsidian, I just don't know if Obsidian truly deserves possibly going through Round 2 with Bethesda.
Which begs the question, why doesn't Bethesda just buy out Obsidian?
Chris Avellone is EASILY one of the most respected writers in the gaming industry, something Bethesda severely lacks. It's also simply a wise idea to hire on the original writers of Fallout, as it's my firm belief that the ORIGINAL artist behind the product is just going to naturally mesh better with the product than a third party. They know the ins and outs of it as they helped create it.
But perhaps the way New Vegas was handled is cheaper than paying Avellone and crew a regular salary like their own employees. If that's the case, I wouldn't be surprised if they DO hire Obsidian to make another Fallout title exactly how they did before. It's definitely profitable for Bethesda, and I think most Obsidian developers answer the question of "would you be willing to work on another Fallout game" with "in a heartbeat." Looking at it that way, I think it's actually fairly likely it could happen again.
As for your question of "does Obsidian deserve it," I think this is one of the uglier sides of capitalism, where Bethesda gets a majority stake in New Vegas' profits simply for owning the rights to the series, and not neccesarily for doing majority work (don't get me wrong, they obviously made the majority of the models, but I think it'd be very pretentious for Bethesda to claim majority work in the project. 50-50? Maybe, but not majority). Nevertheless, I personally would have a lot of respect for Obsidian if they did it anyways, if not for the money, than simply out of a love of what they do. In this case: making Fallout games.