The key word here is "suspect". We live in 2012: if you want to question a suspect you don't have to have him in your jurisdiction to do so. If you don't want to interview him in the embassy or by phone, you obviously don't care. If he doesn't want to talk, that's within his rights, and a refusal to come to your country should be interpreted as such.

The only reasons you would want a suspect extradited to your country are: to press charges and make an arrest, to torture, to make a media scene, or to 'punish' someone by detaining them even though you can't make the case stick.

The only acceptable reason is the first one, in which case you should press charges before extradition.