O'Hare has quietly become one of the stronger transatlantic departure points in North America, and the Chicago-to-Amsterdam corridor is a prime example of why — particularly when you understand the subtle differences between the two carriers competing for your loyalty on this crossing. United's Polaris cabin, operated on the 787-9 Dreamliner out of Terminal 1, remains one of the more genuinely restful business class products across the Atlantic, with its direct-aisle-access seats and the kind of soft-product refinement that the airline has steadily built since relaunching the cabin years ago. The Dreamliner's lower cabin pressure and larger windows make an appreciable difference on an overnight departure, which is the configuration you'll almost always encounter leaving Chicago — wheels up around dinnertime, landing at Schiphol mid-morning.
KLM's offering via its own codeshare metal deserves serious consideration, particularly if you connect through Amsterdam frequently, as the airline's World Business Class seats — while not fully competitive with the very best European products — offer a genuinely comfortable herringbone layout and KLM's characteristically warm, no-nonsense Dutch service. Schiphol itself rewards the arriving business class passenger: it's among the most efficiently designed major European hubs, with customs clearance often faster than you'd expect and excellent Lounge connections if you're continuing onward to secondary European cities.
Seasonally, the shoulder windows on either side of winter — October through early November and again through March — represent the corridor's most favorable booking environment, when premium cabin demand softens after the summer surge and before spring conference season tightens inventory again. January and February, in particular, tend to reward the traveler who plans eight to twelve weeks out.