My recent experience with CO and DL redemptions varies significantly. I have been able to find good inventory, based on flexiblity on CO transatlantic flights at 55K Y or 105 K BF (more effort), or its partners (AC, US, UA) all on line. I recently tried 1 Business ticket for LHR-SAN and DL wanted 270K. Ouch! And here's something else for redeeming travel outside the N. America: DL fees are 4 times more than CO. I just booked 2 tix FCO-LIS-ZRH for 25K and $70 fees a/i on CO. DL wanted 40K in miles+ $248 in fees and a non direct routing (FCO-AMS-LIS-AMS-ZRH). [Cash price was $850]

For the situation described by OP, CO is the winner, no-brainer.

DL only makes sense for lots of domestic travel where upgrades are the priority over redemption.

SQ does JFK-FRA-SIN on a 747-400 with F/J/Y cabins.