Measurable difference between fresh and dried minced garlic

I guess it depends upon the definition of "crushed" If by crushed, you mean using a garlic press, then there is quite a difference between chopped and crushed garlic. When you crush garlic, no need for a garlic press, the flat of a knife and a little salt is all that's needed, you release the essential oils, resulting in a stronger flavour. You can also purée the garlic.

It's also important to consider the type of recipe, in some recipes, such as a pasta sauce, chopped garlic is fine. In Asian cooking, especially Indian cuisine, it's common practice to use minced or puréed garlic. In roast dishes, using the whole cloves in the roasting tin with the meat, can produce an incredible sauce.

Yes, it is different. Does it matter? It depends.

If you're going to use garlic in a stew or anything else that would 'dissolve' the regular garlic anyway, it doesn't really matter all that much in my opinion.

If you want to preserve the texture and/or create a more 'urgent' garlic flavour in short-cooked food, I'd go with fresh.

Sidenote: most of the prepared garlic comes with additives, consider if you want to have those as a part of your diet.

As for keeping time once opened: no worries really - bacteria really don't like garlic all that much, so refrigerated you should have no problems hitting 6+ months.