Does a block of coal or 9 pieces of coal last longer when smelting?
Even though a block of coal is more effective than a 9 pieces of coal, it is worth noting that it can smelt up to 80 blocks, which is more than one stack of items, and therefore more than you can fit in the top slot of the furnace.
You will need to put a hopper on top of the furnace to make sure everything gets smelted, unless you want to camp in front of it and manually add items.
A major difference is that fuel, once "ignited", will be used even if there is no item on top. Which means that if you want to cook 8 items, go somewhere, cook 8 more, leave again, cook 8, and so on, the pieces of coal are more efficient, since only one piece at a time will be consumed, whereas the block of coal would still burn when you're not smelting anything.
A block of coal lasts 80 items. It is therefore more efficient to use coal blocks compared to using 9 individual pieces, which would only yield 72 items.
For reference, a bucket of lava yields 100 items.