There really isn't much of a difference between minced and roasted, nor whole v. pureed, in terms of shelf life. Safety isn't so much the issue but quality is. (This, provided roasted garlic--or any cooked garlic--was cooled relatively quickly then chiled.)
Minced garlic loses it's flavor in short order. I always recommend mincing or pressing a la minute, just what you need. Minced garlic in oil will last much longer, flavor-wise, but it is important to take steps to prevent C. bot outgrowth. This definitely means at the very least, storing in the fridge after combining. Prior steps can be taken too as further safeguards: the garlic can be acidified (toss the minced garlic with lemon juice and allow to macerate a while) before mixing with the oil and fridging; heating before cooling and fridging is another option.
Because roasted garlic is cooked it's safer to begin with. Treat it as you would cooked meat: do not remove it from the oven and place it on the same cutting board or counter it was on before cooking unless that board or counter has been thoroughly cleaned.
I think the flavor of roasted lasts longer than fresh because the key volatiles have already been mellowed--one of the main points in roasting in the first place, of course. With minced, the sharpness goes first and then the high end notes and it gets this lopped-off, kind of flat flavor. Still, spoilage bacteria are the issue when holding in the fridge. They won't hurt you but will alter the flavor.
Freezing is a viable option. What I do is to combine the roasted garlic with something I often use with the garlic anyway and then freeze that. I find it easier to deal with that way. For instance, I make roasted garlic compound butter going VERY heavy on the garlic; log it, wrap, twist, freeze. Then I can cut off what I want to use in something or use as is. Another thing I do is to mix it 50-50 with chicken stock and freeze in cubes. By far, for sauces I combine roasted garlic with chicken stock more than any other liquid, save heavy cream. I also mix it with buttermilk and freeze it that way too--excellent for salad dressings.
I find that doing it this way gives me the best of both worlds. You can, however, mash the garlic well, put it in a container, and freeze it as is. Then you simply remove the lid and scrape the frozen mass with a spoon and it comes off in flaky crystals like Italian ice. I rarely use it in very small quantities so I just freeze it mixed as noted above.