If you get the Pro or Expert version of Alibre, it comes with Algor's Design Check FEA software.
Alibre is also somewhat integrated (I use that term loosely) with Algor in that Algor now prefers Alibre as the geometry creation tool. They still have superdraw, but most tasks are performed by Alibre. So, in short, yes Alibre does have FEA capability out of the box.
"Pits" - That term will have to be more closely defined in order to compare with other software. In general, if pits means crashing and instability, I haven't come across that in Alibre that wasn't hardware related and wasn't easy to fix. For example, I would crash when I had Netscape and Alibre open and I found out it was because my graphics card and NIC were using the same IRQ. Once I moved my NIC to a different slot so a new IRQ was automatically assigned, no more crashing.
If pits refers instead to feature creation or workarounds, then yes Alibre has those. It is a young software so all the bells and whistles aren't there to make feature creation SUPER easy. BUT, there isn't anything I can do in SW or SE that I can't do in Alibre. Then again, I do mostly tool design (machined parts). If I were doing a lot of mold work or consumer product design with swoopy surfaces, then I will have to wait a release or 2 for Alibre to catch up. But again, what some people consider a work around, others consider technique so it really depends on your specific point of view.
--Scott
For some pleasure reading, try FAQ731-376