No. Secondary antibodies most importantly differ in respect to dillution they can be applied at. 
A secondary antibody used in high dilution >1: 25 000 is decreasing the risk of potential cross reactions. 

Such a reagent will last for many experiments, which will secure usage of the same batch over a longer period of time. 

An efficient secondary antibody will also shorten your Western blot time, as 1 h/RT incubation will be sufficient. 

Once you are about to purchase a secondary antibody, pay attention not only to the price/mg or ml of antibody, but carefully check which dilution is recommended for the technique you are planning to use. 

High working dilution is what you should pay most attention to.

Can primary and secondary antibodies be incubated simultaneously? Check here

 Secondary antibody comparison
Agrisera goat anti-rabbit IgG, HRP conjugated antibody (AS09 602) has been used in this Western blot with chemiluminescent detection.

This antibody can be used in a minimum dilution of 1: 25 000 1h/RT. 

The full collection of Agrisera secondary antibodies can be found here