I think that there is likely to be some effect on both, but a key question is how you determine "resonant."

I am familiar with radio antennas in which resonance is a product of the standing wave ratio (SWR) or reflected power when a signal is sent to the antenna.  The surface area of the element affects bandwidth with the larger area providing a wider bandwidth that has low SWR.  Low SWR also provides better signal when the element is used in receive mode.

The conditions you cite suggest that one element might be better than the other, but that both would likely be affected, at least somewhat.

Sorry if this is too superficial an analysis for your question.

Your radio and television work on that principle.

It depends what you mean by a slightly different frequency.  Each object will have a bandwidth over which resonant effects are significant, where the relative bandwidth is close to 1/Q, and Q is the quality factor (2 pi times the ratio of the stored energy to the energy input per cycle needed to maintain a steady state).  If the resonant frequencies are closer together than the relative bandwidth then it is hard to get different behaviour, although, for instance, the phases of the reflections from the two objects would be significantly different even for relative frequency differences small compared to the relative bandwidth.

I'm with Malcolm. All depends on Q. As long as we're being qualitative, the answer would be, "depends on how slight the difference is."

Certainly, if the "object" in question is a TV tuner, then it will resonate much more at the tuned frequency than at frequencies 6 MHz (or 8 MHz) from the center of the tuned frequency channel. That might be considered "slight."

On the other hand, if the object in question is an antenna, you would have a hard time designing one that will respond dramatically differently at fc and fc +/- 6 MHz.

Your application is related to wireless RF, so definitely  receiving objects contain antennas.  

In your question you mentioned that the objects are having a slight variation in resonant frequency.

So. both the antennas will receive the signals (It is difficult to design such a slight varying BW antennas) which you are broadcasting depends upon the bandwidth of the each antenna (strong and weak signals).

If you want to eliminate the effect of a signal on other object (which is not supposed to receive), make use of filters. 

Dear Mr. Mann,

I have not see a measurement description with geoemtric and electric details.

So I can only answer, that this problem can be a problem of the transmission of the electromagnetic field . If the field input geometry is different, so we have different ressonance effects.

All the best

F. Gräbner