Do the firewall hardware specifications have to be better than the network it protects?

If I need a bodyguard cI'll have to hire someone whose muscles are much tougher than mine. If a server can't handle a DoS/DDoS attack because it consumes it's resources does this mean the firewall has to have better resources than the server it protects? ie bigger RAM, better processor and of course this means the firewall cost more money than the server itself? What is wrong about my assumption?