Both decks are made from the same company using the same paper - the only difference is the design and color.
Most of what Magic Orthodoxy wrote is correct and helpful, but the above sentence is factually inaccurate and need correcting.
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DKNG Red Wheels - these are printed on USPCC's "crushed" stock. This means the paper goes through an extra process before printing, in which the stock is "crushed". It makes it softer and handle very smoothly out of the box (which is why cardists love it), but as a result it is not as durable.
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Red Monarchs - these are printed on USPCC's regular stock. Because the paper haven't gone through the crushing process, the deck will feel slightly stiffer than the Red Wheels deck, and not as soft initially. But it will be more durable and last longer.
Both handle well and are excellent quality, but if you want a "softer" feeling deck, that's what you'll get with the Red Wheel deck; if you want something slightly more durable, that's what you'll get with the Red Monarchs.
Personally I wouldn't attach too much important to this, however, and would make your decision more on the visual look of these two decks. The Monarchs have a more standard look, whereas the Red Wheel deck has stunning gold metallic ink and a very different style. I'd suggest you pick whichever deck's looks you prefer, since that is something you'll be seeing all the time when using it, and should be a bigger factor than the handling. Your intended usage of the deck also should play a role, because a deck used primarily for card magic should be more standard, in which case I wouldn't recommend the Red Wheel deck.