Absolutely, the order that index columns are specified matters hugely.

http://sqlinthewild.co.za/index.php/2009/01/19/index-columns-selectivity-and-equality-predicates/

That said, you need to have a look at the queries that use that table and see if both indexes really are necessary. The missing index feature looks for the absolute best index for each and every individual query, it doesn't take more than one query into account when producing those suggestions. You need to do some deeper analysis yourself, you cannot just take those suggestions and implement them blindly.