CONVERT is SQL Server specific, CAST is ANSI.
CONVERT is more flexible in that you can format dates etc. Other than that, they are pretty much the same. If you don’t care about the extended features, use CAST.
EDIT:
As noted by @beruic and @C-F in the comments below, there is possible loss of precision when an implicit conversion is used (that is one where you use neither CAST nor CONVERT). For further information, see CAST and CONVERT and in particular this graphic: SQL Server Data Type Conversion Chart. With this extra information, the original advice still remains the same. Use CAST where possible.