I break this entire topic into two sections - 1) the value of my miles, and 2) credit cards that use mileage rewards vs. cash back cards.
For the value of the miles, I actually make this as easy as possible, following a number of points websites out there, with a simple math equation:
(Cash price - taxes and fees) / number of miles redeemed
Using this year's [economy] tickets in the above equation:
($3,800 - $100) / 420,000 = $0.008/mile
For my flights, this is what I was looking at:
Economy: ($3,800)
MileSAAver: Between 135k miles ($0.027/mile) and 187k miles ($0.019/mile), but only 1 or 2 travel days per 3 months availability
AAnytime: Between 300k miles ($0.012/mile) and 420k miles ($0.008/mile)
Using the equation above, the low end of AAnytime award travel would have made my miles worth $0.012/each, with MileSAAver coming in between $0.027 and $0.019 each. All being better "bang for your buck" redemptions.
First: ($7,987)
MileSAAver: 320k miles ($0.024/mile), but only 1 or 2 travel days per 3 months availability
AAnytime: Between 540k miles ($0.014) and 645k miles ($0.012)
As you can see, MileSAAver awards give you a much better return. I'm basically getting the worst return for my miles, unless MileSAAver awards [in either class] open up between now and my flight, and I call AA to have this changed.
With regards to miles/cash back, let me preface this by saying that a very large part of my AA mileage accumulation is done via Citi AAdvantage Platinum card churning, where I earn large bonuses for meeting a minimum spend in a specific amount of time.
I'm averaging four Citi AA Platinum cards per year, so let's call it 240k miles on $12k spend (assuming I'm averaging 60k bonus miles per card), and then 23k miles/year based on an additional spend of $23k. In total, that's 263k miles/year on $35k spend. I'd be comfortable simply using miles to upgrade to first for these flights, as well, but since I have no status with AA, and because the Hawai'i routes are full, there never seems to be any award upgrade availability, let alone for a party of 3.
Conversely, I'd see the following in terms of cash back redemption using the same annual spend as above:
Citi Double Cash: $700
Chase Freedom Unlimited: $525 + $150
Chase Sapphire Preferred: $525, or $656 when redeeming via the UR Travel Portal
So, given that I'm effectively saving either $3,800 (economy) or $7,900 (first) every time we fly to Hawai'i, using miles just makes much more sense. Granted, if you're relying on normal spend, this is probably not the way to go.
Spoilered below is an estimate of my mileage accumulation over time, where it appears as though I'll be able to fly using miles for the foreseeable future. Each month adds 1900 miles, with an additional 60k miles quarterly from a new card bonus.