Metal or Carbon Resistors - Which is better?

Neither, I usually use carbon film, at least in the signal path, Vishay, TE or Takman.

Always tradeoffs, but per the recommendation of an audio buddy I went with the Takman REY metal film in my Hagerman Bugle 3 phono stage.  No regrets, and will likely use them again when I build the Hagerman Cornet 3. . 

I wanted to share my resistor preferences for different applications.

I prefer using tantalum resistors in signal paths and cathodes.

For power supplies, I opt for metal film resistors.

Lastly, for loads, stoppers, and speaker crossovers, I find carbon resistors to be most suitable.

Not sure about "better" but I chose Amtrans AMRG non-magnetic carbon film resistors in my Hattor passive that I use to adjust volume and provide a display and remote control in my system.  I have been happy with the sound, and compared to the many other preamps I have owned I don't believe it leaves anything on the table wrt volume control without gain.

What resistor sounds best very much depends on application.  After several decades of comparing resistors, I have strong opinions on the subject.  A short summary:

For loads (input, interstage and output), Audio Note 2w silver tantalums.  The 2w silver sounds better than 1w or 1/2w.

For gridstoppers, Riken carbon film (discontinued).

For phono RIAA eq, Vishay bulk foil.

For plate loads and power supplies, Mills wirewound.

I don’t like some of the other resistor types mentioned above such as AMRG and Takman, and I haven’t had any luck with vintage Allen Bradley’s.  However, there is one other type that is a solid second or third choice to my favorites listed above, namely, Dale/Vishay CMF metal foils.  The Dales are cheap and readily available in lots of values.  They have a warm, musical sound with good detail and dynamics.  Take a look inside a Lamm preamp or amp and you will see Dale CMFs throughout.  Same with older Cary amps and preamps.