I'm going to bite my tongue here, as we all know my (exceedingly low) opinions of Mrs. Clinton and her disastrous Presidency. I don't think Obama is quite the savior this site and the left in general have made him out to be (I've read far, far too many TLs where he's a messiah who single-handedly saves America and the rest of the world), but perhaps it would have been better.
Anyway, we might not go into Libya and Syria guns blazing like we did OTL, seeing how Obama was much more anti-intervention than Hillary was. As a result, we might avoid a nuclear Iran - both Obama and Hillary supported a nuclear deal, but the latter's actions in toppling Assad and her management of the Persian Gulf Incident destroyed pretty much all the goodwill we had in Tehran. Noninterventionism in the region might have also prevented the ongoing migrant crisis, as well as the Wave of Terror. As a result, we might not see a Pence presidency in 2016; as you recall, one of the main reasons he was able to make it as far as he did was because of public anxiety over mass migration after the attacks in Paris, Brussels, Berlin, Nice, and the Mall of America; not to mention the riots in Hamburg and Stockholm.
We might also avoid the Long Hot Summer of 2013. For all his faults, and despite his association with that crazy pastor, Obama gives me the impression that he would have been a unifying figure after the incidents in Raleigh and Atlanta. Hillary, on the other hand, wasn't trusted on either side of the racial divide, and her attempts at calming one side would only infuriate the other, and we saw how bad things got before it was over.
However, I still feel like we'd see things like the attempts at gun control and healthcare reform, with the same results. I also think you would still have seen the Russo-Ukrainian War like IOTL; a revolution against the pro-Russian government was bound to happen, Hillary or not (regardless of what RT says), and I doubt Putin would have responded any differently. Obama might have avoided the Black Sea Missile Crisis, though.