So here is the scenario:

 You are making a leaf keychain. You are forging on your main shop anvil with your favorite forging hammer. You start to forge the taper on the edge of the anvil, when you suddenly miss the steel and hit your anvil. Would you rather your anvil or hammer to get damaged?

To quote my old friend Al, when asked whether it was worse to drop your ice cream on the ground or to have to watch your balloon drift away into the sky:

They both suck.

I would rather neither get damaged. I would practice hammer control and patience to avoid this scenario. That said, mistakes do happen, but if it came down to it I would rather damage the hammer face. Hammers can be much more easily dressed than an anvil face. If you chipped the edge of your anvil it is most likely because you left the edges too sharp. 

Take your time. You don't need to forge as fast as a farrier in competition to make a something. 

Hammers are typically easier to dress and typically easier and cheaper to replace. 

You wouldn't ask that if you owned a Soderfors, hammers always lose though you CAN chip an edge. Don't miss, by time you're down to thin you should be using lighter blows so you should be much more accurate.

You just need more practice, making nails is excellent practice for making consistent tapers and heading. You can't be consistent without good control and it's a good gauge of your progress.

Frosty The Lucky.

Definitely hammer.

Next would you rather!

Would you rather burn a piece made of cheap mild steel you've been working on for an hour,

or

burn a piece of expensive steel on the first heat? 

You can forge yourself a new hammer, try making a new anvil.

How  expensive ?

 

 

 

It's all relative.  Expensive for you.

I have never chipped an anvil but I use Swedish cast steel anvils. Kohlsva and anonymous. It is possible to chip them, however, someone has  - perhaps missing with a sledge hammer?.

Yeah you can chip the edges if you're ham handedly and apeish enough.

Frosty The Lucky.