There have been a few little bits of BB-8’s vocalizations that I’ve heard in trailers and such, and it sounds fairly different from R2-D2 in terms of the “voice” but I couldn’t hear enough to figure out if it’s still the same actual language that R2 speaks. I assume it’s some version of “Binary” but I wonder if they are identical languages?
Not quite. But it’s a more advanced version of “droidspeak.”
According to Star Wars: The Force Awakens Visual Dictionary:
BB-8 converses in 27th generation droidspeak code, a compressed variant of the most common astromech language
Also, please note that out-of-universe they specifically worked to make BB-8 sound more "human" like, with a Voice Consultant and a live voice actor.
I have to credit DVK with posting this, but he has the eBook version of The Force Awakens novelization by Alan Dean Foster and there is definitely a clue as to the language/dialect that BB-8 speaks. The scene describes when BB-8 meets R2-D2 at the Resistance base; bold emphasis is on the droid language part of this:
In the dark, dusty storeroom he rolled over to the R2 unit and beeped a greeting, the transmission sequence too rapid and too exhaustive for any human to follow. It didn’t matter. There was no response from the immobile R2 unit.
BB-8 tried again, utilizing a different droid language. When that also failed, he moved forward and gave the other mechanical a forceful nudge. Like everything else, that too failed to generate a response.
So it is clear that BB-8 is fluent in a few different droid languages/protocols. And I am assuming that BB-8’s initial “beeps” were in it’s default language and it then “switched gears” to some other language.
UPDATE: I just saw DVK’s comment on the original question here and will gladly accept a “defeat” to this answer if DVK can dig up something more concise or more detailed than my simply swiping an excerpt that was previously posted.