My previous employer had a similar policy that worked two ways: (1) If you took a connecting flight vs. a direct flight, you got 60% of the savings as a check, and (2) If you stayed over a Saturday night, you could spend up to $100 less than the non-Saturday-night-stay fare on lodging, entertainment, meals, etc.
I took advantage of the second option many times for fun weekends in interesting places on their nickel. I never did the first because at the time the savings wasn't that great, and those checks are taxed as ordinary income, so the difference in my pocket was seldom worth the time spent. In the example by the original poster, I'd certainly take the $$$, because it is significant (even after taxes). In my cases, it always seemed to save $150 before taxes, so 150 * 0.60 = $90 * taxes = $40-60 = not worth the three hours.