Why do some EMI/RF shields have holes on the top and some don't?

Advantages of holes in shield:

1. Allows some air flow for better heat dissipation. This is the primary reason.

2. Less weight.

Small holes don't really compromise the shield, as long as the holes are significantly smaller than the wavelength of what you want the shield to attenuate.

As a aside, you won't ever see long slots in RF shields. If a larger overall opening is desired, it will be accomplished with a array of holes. The shield is then still a mesh in that area, which is mostly as good as solid, as long as the individual holes are small compared to the wavelength.

A single long and thin slot is actually a antenna. Imagine a conducting sheet with RF current flowing in one dimension. A slot perpendicular to the current flow has the same characteristics as a dipole antenna. In fact, such things are called slot antennas. Obviously it would be bad to add slot antennas to something intended to be a shield.

Good answers here already but I would also add, holes also significantly change the thermal/mechanical properties of the shield.

As you know, when metal gets hot it expands, similarly, it shrinks as it cools.

If a "can" type EMI shield is soldered down to the PCB, and said shield is solid, that will introduce a significant difference in expansion rates between the PCB and the shield.

This can cause effects like:

1. Failure of the solder joints holding down the shield,
2. Tearing the solder down pads off the board,
3. Warping of the board, with possible resultant intermittent/failing connections elsewhere,
4. Audible popping of the shield as internal stresses are redistributed. (This can also introduce a concussion shock to the joints and PCB.)
5. The shield to dislodge.

This can be a significant issue if the EMI shield is soldered down during normal manufacturing where the boards are pre-heated before the solder flow phase. When the board cools again, a residual stress will be introduced. Boards can actually come out with quite the curve or warp in them.

Shields with nicely laid out holes also look much "cooler".

Providing holes will provide shielding while saving on material costs.

Presence of holes doesn't mean that RF signals will pass un-attenuated. There is a cut off frequency for the given perforation dimension. In terms of wavelength, it becomes:

Cut off wavelength = 3.142 * radius of hole (for circular perforations)

For a 2.4 GHz wave, wavelength = 12.5 cm

Thus a hole smaller than 12.5/3.142 cm = 3.98 cm in dia will attenuate the RF signals.

In a lot of cases, shielding is required against 50/60 Hz line noise or some hundreds of kHz noise coming from a switching regulator. In this case, even a much bigger hole can provide shielding while effectively saving on material costs and making the system light-weight.