CONVERT is specific to SQL Server, and allows for a greater breadth of flexibility when converting between date and time values, fractional numbers, and monetary signifiers.

CAST is the more ANSI-standard of the two functions, meaning that while it's more portable (i.e., a function that uses CAST can be used in other database applications more or less as-is), it's also less powerful. CAST is also required when converting between decimal and numeric values to preserve the number of decimal places in the original expression.

For those reasons, it's best to use CAST first, unless there is some specific thing that only CONVERT can provide in the work you're doing.