It would depend on so many things. Did I have plenty more miles, or were these my last miles? Did I have plenty of money, or would paying $3400 put me in debt? (Going into debt -- unless you happen to "isolate" it on a never-otherwise-used card at near-0% interest -- so wipes out the value of CC rewards that it's pointless to earn CC rewards and be in debt at the same time.) Was this a one-time trip, or just my yearly trip?

I have accumulated way more miles (across multiple programs) than I need in the short term, and meanwhile don't typically have $3400 spare cash, and so for me I'd use miles at a poorer rate if needed because spending that much cash would be too hard.

But someone else may be in the opposite situation.

And accumulating big amounts of miles from credit cards is getting harder by the year, so you can't count on replenishing miles you earned a couple years ago as easily the next time (if you're not flying for business and earning most of your miles that way).