I see in the photos of the attenuator you linked to that it is marked "-20 db at 600 ohms," and that some of the comments and questions near the bottom of the page indicate that it is apparently intended for use with professional microphones.
If 600 ohms is its input impedance, that is of course much too low to be an optimal load for the line-level outputs of many and probably most audiophile-oriented components.
If 600 ohms is the load impedance it is intended to work into when providing 20 db of attenuation, that would suggest that its input impedance is probably something like 6K, which is still to low to be optimal with some audio components, especially many that are tube-based.
Like the previous poster, I too have had excellent results with the Rothwell 10 db attenuator (in unbalanced form in my case), but some other experiences with it that have been reported here differ.
Also, I’ll mention that resistance measurements I’ve taken of the 10 db unbalanced Rothwell attenuator show that it consists of a 22K resistor in series between its input and output, and a 10K resistor in shunt between its output and ground. Therefore, depending on the input impedance of the component whose input it is connected to, the component providing the signal to it would see a load impedance in the rough vicinity of 30K or so, which is a reasonable number. While I recall that another member reported that the corresponding numbers for a 12 db attenuator made by Harrison Labs are far lower, about 6.75K in series and 2.2K in shunt. The latter numbers are low enough to be a problem with some components.
Regarding the Shure attenuator you referred to, if that is the model A15AS it is also intended for use with microphones, and it has a specified input impedance of 1K. Much too low to be an optimal load for many and probably most audiophile-oriented components.
Rothwell offers a 20 db balanced attenuator, as well as 10 and 15 db versions. As I see it you are much less likely to go wrong with one of those than with any of the other alternatives.