There is significant evidence that the two universes are not the same.
Timelines.
It's important to establish that the bulk of Avatar takes place approximately 30 years after Alien and that the Alien Universe covers this entire time period.
Avatar opens in 2148 and takes place largely in 2154. By comparison, Alien opens in 2122 and finishes with Ripley fighting the Xenomorphs in Aliens in 2179.
FTL
Despite its later setting, FTL travel doesn't exist in the Avatar universe (although FTL communication does exist). By comparison, faster-than-light travel in the Aliens universe has been commonplace for decades.
Talk of “wormholes” and “warp drives” captured the imagination of twentieth-century sci-fi fans, but no such methods have come to fruition.
Engine technology.
The engines on the Venture Star use matter/antimatter annihilation to generate power and thrust (up to approximately 70% of lightspeed). By comparison, ships in the Aliens universe use fusion reaction and something called a 'tachyon shunt' to achieve FTL speeds. Even small vessels like Ripley's escape shuttle are fitted with these kinds of engines.
Weyland-Yutani vs. RDA
Within the Avatar universe RDA are described as being (in 2154) as
The largest single non-governmental organization in the human universe.
This conflicts directly with WY's position as the largest of the mega-corportations from a period stretching from the 2100s through to at least 2179 and beyond. Simply put, they can't both be the largest company ever.