Without having an actual Spartan-6 LX150 board on hand, I ran my design through ISE quickly. This showed that the LUT consumption is indeed similar to Altera's, so there does not appear to be any area improvements by using a Xilinx device over Altera.

What I do not know, however, is how fast Spartan-6 LUTs operate compared to Altera's, for apples-to-apples speed grades. If they run faster, it would indeed be possible to get more bang for your LUT. I get 80MHz in my design, resulting in 80MHash/s burning 80K LUTs. The Cyclone4-150 or Spartan6 LX150 may fit two full hashing pipelines (128 SHA-256 rounds per full hashing pipeline). This would double their performance. The Cyclone4-150 achieving 160MHash/s. If the Spartan6 is faster, it could possibly achieve >200MHash/s as you've reported.

You could get faster speed grades, but those are typically a bit more expensive. I haven't calculated whether a fast speed grade would balance out the cost for its improved hashing speeds.