The difference is the following:
xs:int is a signed 32-bit integer.
xs:integer is an integer unbounded value.
See for details https://web.archive.org/web/20151117073716/http://www.w3schools.com/schema/schema_dtypes_numeric.asp
For example, XJC (Java) generates Integer for xs:int and BigInteger for xs:integer.
The bottom line: use xs:int if you want to work cross platforms and be sure that your numbers will pass without a problem.
If you want bigger numbers – use xs:long instead of xs:integer (it will be generated to Long).