sfwcl installer automatically creates AMD_FX.bat file in Crysis directory so you should use it. Compatibility mode is usually needed only for 64-bit version of Crysis. Running it as Administrator is good idea because map-downloader probably won't work without it (enabled UAC causes this problem).
If the AMD_FX.bat doesn't help you, you will need to modify it - open it in Notepad (or any other simple text editor) and change /affinity FE to:
- for 4-core AMD FX processor => /affinity 0E
- for 6-core AMD FX processor => /affinity 3E
- for 8-core AMD FX processor => default value should work (/affinity FE)