Basically the difference between the two comes down to parameter sniffing. At compile time the optimiser can see the value of the constant and can compile a query plan optimal for that value. This is called parameter sniffing. It is a Good Thing (most of the time).

When using a variable, the optimiser cannot sniff the value at compile time (the variable has no value at compile time) and hence the optimiser cannot use the value of the variable to generate a plan optimal for that value. It generates a more generic plan. In some cases this generic plan will be less optimal than the plan compiled with parameter sniffing.

The other side of the story however is that a generic plan may be better for reuse than an optimal plan, if the number of rows that the query affects can change radically between multiple executions. This is because in both cases the plans will be cached and reused.

Have a read through these, they're not as detailed as they could be, very old posts. If you want more information, google "Grant Frichey" "parameter sniffing", you'll find some of his articles on the subject.

http://sqlinthewild.co.za/index.php/2007/11/27/parameter-sniffing/

http://sqlinthewild.co.za/index.php/2008/02/25/parameter-sniffing-pt-2/

http://sqlinthewild.co.za/index.php/2008/05/22/parameter-sniffing-pt-3/