consider these:
1. 1 amp across an mur860 fred will cost you 600 to 1000millivolts or 600 to 1000milliwatts loss!
a 5U4 with an output of say 100mA will cost you 5v@3amp or 15watts plus about 4watts plate loss!, so which one is better?
2. on the transformer side on things, traffo supplying the 5U4 rectifier will always be center-tapped! as against a full-wave bridge for the mur860! a full-wave center tapped traffo will have one leg conducting, per electrical cycle, whereas the full wave bridge uses the traffo winding for the full cycle. thus half of the time half of the center-tapped traffo is doing nothing! therefore, transformer utilisation is better with a full wave bridge than with a center tapped one! a full wave voltage doubler otoh can give even higher voltage and needs only 2 diodes against 4 for the full wave bridge and transformer utilisation is the same as that for the full wave bridge plus voltages on the traffo will be lower. i remember as a child i would put candles on top of transformers and watch those candles melt with glee! LOLZ!!
3. as to which sounds better? i can not see any basis in science to claim that tube rectification sounds better than ss one nor vice-versa. the psu has only one reason for its existence, that is to convert ac to dc with minimal ripple components as possible!
4. imho the best power supplies would be batteries! they have no ripple components to begin with and has a very low internal resistance, but size and costs and practicality will prohibit their use!