Your best bet is flying across the Atlantic, where the Strategic Lateral Offset Procedure (SLOP) is used.
This is where the pilot flies a offset to the route, either 1 or 2 NM, always to the right, chosen randomly (or based on surrounding traffic/TCAS), and is kept from the ATC (no radar coverage, although that is changing with satellite ADS-B).
As shown below, you have a chance to see another plane above/below from either side depending on the pilots' flip of coins.
Regarding two-way airways elsewhere and with the navigation paradox, where flying accurately is ever increasing, it will be a slim chance except for a crossing traffic (not same airway).
If in a holding pattern, the standard turn is right turns, so the right side gives a better look "inside the track," unless the pattern is non-standard to the left.
Source: Mid-Atlantic Race!!! Virgin Atlantic A340 vs Norwegian 787 Dreamliner