Windows vs Linux tool set

As for equivalence, it depends on how good you set your timing requirements. As Quartus will produce a different placement and routing, the resulting configurations will have different timing. If you have completely defined your timing requirements and Timequest says in both cases that they are met, then you can say that both bitsreams are equivalent. But if you forgot some requirements, or if some have a wrong value, then you could see a difference in timing between a configuration generated from Windows and one from Linux.