Electrically, regardless of source type, if you have any isolated voltage sources that can't feed back into each other (diodes in series with them anywhere in their current path prior to connecting to the other source(s)), then:
--lower voltage sources are effectively "disconnected" because they can't cause current flow, and can't receive current flow back into them from a higher voltage source past the diode.
--highest voltage source will provide all of the current flow.
So...if you have isolated voltage source panels, then only the highest voltage panel will contribute anything.
If you're dealing with current sources that change resistance but not voltage, always generating the same voltage, but changing current because of changing resistance, then they could both contribute current.
So if your panels are current sources, they could both contribute whatever current they can generate (may be dependent on the load or converter).
You can test what happens by putting ammeters in series with each panel, and voltmeters across each panel, pre-diode. If you get current from both at the same time, regardless of panel voltages, then they are current sources. If you get current from only one, you'll see that it has a higher voltage than the other, and they are voltage sources.
If you had diodes on those hypothetical batteries, they wouldn't feed back into each other either, and the lower one would not contribute; etc, because they are voltage sources.
If you had unequal LED PSUs (or other constant-current sources), then they could both contribute even if using diodes.
More info on the concepts:
If you can instead series those panels, then you'll get output from both of them regardless, if your converter can handle the max series input voltage at max insolation of the panels.
Disadvantage is that shading either panel decreases current flow from both of them.
With them paralleled with diodes, I also don't know what your specific charge controller will do for tracking (if it's an MPPT or other tracking type), as it tries to adjust to the different and changing conditions on each panel, or if it will react to them as if they were a single panel.
FWIW, BuildItSolar is a good resource for specific panel/converter/etc information (more of it there than here).