Which Database (MySQL or MS SQL) would work better in Windows Server
2003 for an e-commerce site. Main requirements are: stability and data
processing speed.

you are comparing Apples to Oranges here, MySQL is free and is very
usefull in content management system, data access is very fast and has
very good stability. MS SQL will cost you lots of money, is also fast
and has good stability. So selection of database is usually based on
content and how much your data will grow in time. Any database will be
fine, accessing and stability depends on how you write your code and
design tables. In summary, i would see the data content, growth and
budget to pick one.

Sql Server is much better than MySQL, and is optimised to run in a
Windows Operative System,

They're a lot of articles comparing this two databases, 

http://web.zdnet.com.au/builder/architect/database/story/0,2000034918,20272967,00.htm

http://www.mssqlcity.com/Articles/Compare/sql_server_vs_mysql.htm

you can search by "mysql vs sql server" in google.

My suggest is that if the price is not a problem you must choose Sql
Server, is more scalable and stable, you can see also a comparison
between systems in http://tpc.org

TPC is an organism that test a huge variety of systems in an
transactional environment. Members of this organization are Microsoft
/ Sun Microsystems, Oracle, ....

if the cost of sql server is a problem they're a free version named
MSDE , this is the SQL-Server core without administrative tools.