First, there is no such thing as monochromatic light. Even lasers have a finite bandwidth.
All things equal, the best situation is if the bandwidth of your absorption band significantly exceeds the bandwidth of your incident light. Or, put another way, that the absorption feature is locally "flat" over the region spanned by the incident light - a situation that is easier to accomplish if the spectral bandwidth of the incident beam is small (less polychromatic). If the bandwidth of your absorption band does not significantly exceed the bandwidth of your incident light, you will observe deviations from the Beer-Lambert law because you will have complex and nonlinear interactions between the incident beam, which consists of different wavelengths of light with different powers, and the absorption band, which consists of different wavelengths of varying molar absorptivity. The same thing is observed when, for example, you are trying to measure the absorptivity at the side of an absorption band, where the extinction coefficient of the absorption spectrum changes rapidly as a function of wavelength across the spectral area of the incident beam.
There’s a really nice Applet that allows you to play around with this effect and see how varying degrees of spectral bandwidth affect deviations from ideality.\
http://195.134.76.37/applets/AppletBeerLaw/Appl_Beer2.html(There's also an instrument issue for broad spectral bandwidths - and that is that point measurements using a simple photodiode are often not calibrated to take into account different sensitivities of different light wavelengths.)
The originally posted question isn’t a very good one, because there are also other considerations than just the deviation from Beer’s Law that you may have to take into consideration, most notably the concentration range over which you are likely to be measuring. Although it would seem to make sense to always pick the strongest peak, in some situations it is actually better to pick a weak peak. For example, if the concentrations you will be measuring are very large, picking a strong peak (strong meaning high molar extinction) could bring you into a range where the instrument doesn’t perform well – e.g., where the absorptivity is > 1 OD. In such a situation, a weaker peak would be a better choice. (You could also simply dilute the sample or use a smaller path length, but there are drawbacks to both of those options as well.)