Note that, in general, Cyclone III is a superset of the Acex1K family. You're going to be able to do a lot more with it. DSP blocks, PLLs(I think), much more performance, many times the logic for the cost, etc. The only possible thing I can think of is that I think the Acex1K family allowed asynchronous reads and writes to memory, while CIII is all synchronous. If this was done, it's usually not a big deal as there are nearby registers that can be absorbed, although it may require some user tweaking.
My guess is that more than 95% of designs created for the Acex1K family will compile directly into Cyclone III, so you should be fine. If you have a problem, it's most likely something easy to fix.