Coins are better from a practical, economic perspective. It is true, if there were no politicking, the $1 note would have been long gone, replaced by the more efficient $1 coin. The BEP and Crane Co. of Massachusetts, and their contacts in the government, have seen to the continuance of the $1 note.
From a design perspective, I tend to like the idea of a $1 coin better. However, the currently-minted designs are the equivalent of numismatic clip-art; they're awful designs. There are some great historical designs, though, and some great concepts for future $1 coin designs by new sculptors.
Personally I want both a $1 note and coin to be issued for historical/sentimental reasons. I love the idea of ancient-looking currency still being issued, and the $1 note is ancient looking. It's like a time warp, and I want historical relicts like it to continue. But from a similar vantage spot, coins are the more ancient of the two forms of money (paper and metal), so for historical and practical reasons the coin should continue as well.
Now, from the most important vantage point - how money influences the economy, my perspective is this: The solution to any and all monetary problems is to repeal the legal tender laws and allow for competition in currency. According to the Constitution "no state shall make any thing but gold and silver" legal tender - that is the supreme law of the land, and it is still on the books! Given a choice - I'd let you keep your $1 FRNs and your $1 coins too! Keep the lot of them! As for me, I'd only do business with places that accepted a competing currency tied to a commodity basket (gold and/or silver and/or other commodities), and I'd only work for this currency as my wage too.