After supplementing my background (mechanical engineering) with some quick googling to verify what I was thinking -
One definite reason the same frequency will sound different is the shape of the wave. Frequency tells you NOTHING about the actual shape of the waveform itself. If you have a perfect sine wave it should sound different than a sawtooth waveform or an imperfect sine waveform or a squarewave form, etc.
If each speaker was capable of creating the exact same waveform (shape, frequency, amplitudes) and the speaker case, either a box or whatever the speaker was contained within, had identical acoustic properties (they never will be exactly the same for this purpose even within the same brand) you should get the same exact sound.
They can't however. The more advanced speakers presumably can more accurately match the recorded waveform. Unfortunately, physics exists and there will almost always be difficulties in matching a given signal. For example
If the sound waveform being given to the speaker is the blue waveform, differing speakers will have difference responses - indicated perhaps by the differing curves. It is physically impossible to instantly reproduce a given waveform. It just is. By the way, the above graph is from a PID controller in case anyone is wondering, which while technically not limited to audio, the principle applies to nearly any waveform replication. This example is probably far 'worse' than most speakers would be.
Each replicated waveform will have imperfection when compared to the source signal. This will lead to the waveform sounding different, even for the same frequency. Speakers will tend to react to the source sound in the same way consistently - which will result in different sounding "tone" for speakers, ie bright or deep or however else you want to describe them. This is partially (perhaps completely) caused by the speaker output varying similarly to the above graph results varying.
Not to mention the fact that even if two drivers can reproduce the exact same waveform from the exact same source signal the container they are in will likely affect the sound too. Or that the input signal to the speaker will in no way be as simple as a step function waveform (the blue waveform in the above image) considering it will have a lot more instruments, vocals, etc.
Your comment regarding coke/pepsi is actually a really good one. For some people, they can quickly discern the difference between the two. Many if not most cannot depending on the test conditions (as an aside, if you think you are good at this, have someone take the typical test with a twist - instead of 1 cup of each, have 2 cups of 1 and 1 of the other, for a total of 3 cups, and see if you can still replicate your success) can not do this. And obviously, someone who has drank more pop would be far more likely to succeed than someone who drinks pop on a semiregular basis. I would probably fail at the coke v pepsi test.
However, speaker evaluation can be similar. My background involved me playing trumpet in a very good youth orchestra. My ears and mind are acutely tuned as a result (or so I think, hah!) to hear differences in sound. In an orchestra setting, tone makes all the difference. I bought Polk speakers because I listened to a variety and found that to me, Polk speakers were very defined - this is likely a turn off to some people, as it might be too bright, etc. Anyways, the point is people have different talents for finding differences in things they are familiar with. A machinist can probably look at different plates of steel and identify them far better than either of us. Just the same, those more experienced and versed in speakers can definitely see the differences.
It might be more difficult for you than others here. This is, afterall, a forum for people who like this sort of thing greatly and are much more likely to have invested huge amounts of time/money into listening to speakers and therefore have a much larger knowledge and experience base than you.
Anyways, this turned into a book, but this should answer all of your concerns regarding speaker differences. If not I guess I would suggest reading through it again.
edit - You might also be interested in reading about Fourier series based on your discussion of sine waves on the previous page.