I strongly suggest trying to find someone with the speaker of interest already on hand. Try before you buy, or you may have an expensive item you really don't like.
And you're right that you will not remember the fine differences after you get one speaker out of the cabinet and install the other.
There is an option, but it may only apply well to Weber speakers, unless you can find frequency curves for other speakers. Somewhere, I have an article in which a guy describes a recording and/or playback program which will allow you to do some detailed EQ adjustment. You take a sound sample with which you are familiar, and run it through the program with the EQ curve of your speaker in effect. You will need (likely) some good headphones, because you computer's internal or desktop speakers will likely color things significantly. Next, you input a different EQ curve matching the new speaker of interest. Compare the sonic difference of the two.
You will probably know what you're hearing in your present speaker that you don't like. You can compare the changes audibly before buying the new speaker. However, this method will not tell you things like how the speaker responds at a given amount of power input (speaker distortion).
Unfortunately, it requires that you be able to obtain frequency curves for your speaker of interest. Maybe you can find them, or maybe you can't.