A block of wood
Will act as a guide to help hold the work piece tight to the fence/bit to ensure that your cut is consistent. This is good.
Will require precise alignment with the fence. If it is slightly out of parallel, you'll end up pinching your work piece.
- At a minimum, this will stop you from further routing until you get it adjusted.
- At worst, it could allow the bit to grab the wood and kick it back at you. This is bad.
Will also provide a fairly large contact surface against the work piece, so the further you push the work along the block, the more friction you're going to get, making it more difficult to push.
- Having it be more difficult to push means that you're moving slower which could lead to burning.
- It also means that you're putting more force into the feed which could cause you to slip/lose your balance/lose control which puts you at risk of injury. This is bad.
A feather board
Will act as a guide to help hold the work piece tight against the fence/bit to ensure your cut is consistent. This is good.
Has some springiness in the "feathers" which will help provide pressure without perfect alignment of the feather board. This is good.
The springiness of the "feathers" will push the work piece against the fence should there be any amount of back feed, giving a greater chance of trapping the work piece should it, for any reason, start going the wrong way on you. This is good.
The contact point between the tips of the "feathers" and the work piece will remain fairly small and provide minimal friction and resistance against your efforts to feed the piece past the bit. This means that your feed effort will remain reasonably constant throughout the milling operation, improving consistency of the work. This is good.
Is a feather board necessary? No. Neither is a block of wood. Many people operate their router table without either in place and get very satisfactory results. People operate routers without a table (or any sort of guide) at all and get satisfactory results.
Adding one or the other may well improve your work quality, safety, and, possibly, speed of work (it takes a bit less mental & physical effort to keep the work against the bit with something mechanically holding it there beyond just your fingers, so you can work a little faster).
To be honest, I've never heard of anyone using "a block of wood" on the router table other than the one being routed. With that in mind, it's probably better to leave that off the table (so to speak ;) and go with a feather board.
Feather boards do not have to be commercially purchased. You can make one out of a scrap of
2x4 wood (any dimension should do, just make it long enough to be able to fix it in place) - simply cut several slots into one end (a table or band saw would make this easier), leaving 1/16" to 1/4" between the slots (they don't have to be precise), then cut the feathered ends at an angle of your choosing (this is the Norm Abrams/New Yankee Workshop early days method). If you want a fancier one, I found some directions at this LumberJocks thread (no endorsement, just the first homemade instructions I came across). I'm sure you can find other methods of making them, too.