Holes per-se are not usually a big problem. They are generally pretty small, so at the frequencies of greatest interest (usually < 1 GHz), they have very low leakage. Long seams are a problem (even if extremely thin), but not your average 1/2" - 3/4" diameter hole. There are higher frequency signals (wifi radios, PCIe/SATA signaling, cpu cores), but those are usually well confined, individually shielded -- for instance, most wifi radios come as shielded modules with an antenna output. I am not saying you can't have EMI problems at 5 GHz, but more often you get into trouble in the 100s of MHz.
The problem with holes is that you usually have wires going through them. Wires act as antennas if they are not properly shielded, grounded, and filtered. In particular, you really want to have your cable shields electrically connected to the enclosure right at the point of penetration, otherwise it can conduct noise from inside the enclosure to the outside.
So I don't know if holes on the same side vs. opposite side are technically worse, but it is a relatively minor issue compared to what you do with your cables and their shields.