Over the years, I have read several detailed tests in car magazines like Road & Track regarding the performance of engines "designed for premium fuel" that tolerate regular fuel (presumably due to anti-knock sensing in their engine management systems). These tests carefully compared power and fuel economy using premium vs. regular fuel and showed actual dynanometer plots. Unfortunately, those articles do not appear to be available on the web and I discarded my car magazine collection a few years ago. For normally aspirated engines, the impact of using regular gas was small: 1-3% loss of horsepower and no detectable difference in fuel economy. Pinging with regular gas was not a problem. Note that using regular fuel does not force the anti-knock sensor to retard the timing under most circumstances. In the old days before computer-controlled engine management and precise fuel injection, engines that knocked did so under certain conditions (typically high load and low rpm).
The only legal difference between fuel sold as premium vs. fuel sold as regular is octane, which is not a measure of fuel "quality". Years ago, there was slightly more energy per unit volume in regular gas than in premium gas; the compounds that were blended to create higher octane gas had less energy than the gasoline they replaced. The simplest and cheapest way to raise the octane level of gasoline is to add more ethanol (which has a high octane rating but contains less energy per unit volume than gasoline). But government regulations now force nearly all gas (E85, which contains 85% ethanol, in not gas) to contain about 10% ethanol; more exotic compounds with energy content close to that of gasoline are used to raise the octane rating. So the energy contents of regular and premium gasoline are very close and depend on exactly what compounds are used to raise the octane level.
Major oil companies like Chevron, Shell, and Exxon advertise that they put more additives (e.g., polyetheramine [PEA] sold under various brand names including Techron) in premium fuel than in regular fuel, which is probably true. But the EPA mandates the same minimum additive levels in regular and premium fuels so it difficult to know whether an engine is really getting extra additives with premium fuel---particularly if the fuel is not "Top tier". I believe most of what the major oil companies say regarding fuel quality. "Top tier" fuels are generally better: more carefully made with superior additive packs. For this reason, I would feel much more comfortable running a car for which regular gas is acceptable using "top tier" regular gas than off-brand (e.g., Costco) premium.
The best online discussion of regular vs. premium that I have seen can be found at cartalk.com: Premium vs. Regular | Car Talk
Let me back up my opinion with a bit of personal experience. I own a 2007 Honda Civic SI Sedan. For MDXers who never deign to enter a Honda showroom, the Civic SI is the only credible successor to the now defunct Acura Integra GS-R. My Civic SI has a power band very similar to the 1996 GS-R that it replaced, but a higher redline and a little more horsepower to go with it. I ran my Integra GS-R on regular for the last five or six years that I drove it with no detectable ill effects.
The gas cap on my SI says "Premium Fuel", but if you read the fine print in the owners manual, any fuel above 87 pump (or AKI) octane is satisfactory. I bought my car in January 2007 and I have run at most 3 or 4 tanks of premium fuel in the car since I bought it. I cannot tell any difference between regular and premium despite the fact i routinely wind the engine to over 7000RPM (the Civic SI has very little torque but it is fast if you drive like a crazed adolescent). Am I sacrificing some performance? Almost certainly. Based on the magazine tests I have read comparing engine power curves on a dyno, I am probably losing .1 to .2 seconds in a full throttle 0-60 run. But I rarely engage in full throttle runs to 60 mph; it is hard on the clutch. (The Civic SI is only available with a 6 speed manual transmission. Automatics cannot cope with an engine that is a slug at 3000 rpm and a screamer at 5000rpm.)
I do not yet own an MDX but my wife dearly wants one and the 2014 model is almost fuel efficient enough for me to justify buying a FWD model with almost no options---particularly when I take into account the value of marital peace. The most logical alternative is a Honda Odyssey EX-L, but it is far larger than what we need to accommodate a family of five not-very-big people. Moreover, my wife suffers from minivan phobia and she would much prefer to drive almost anything other than a minivan. I can empathize; she has been driving a 2003 Mazda MPV for the past decade.
My family and I are spending this calendar year living in Sweden. If we were living permanently in Europe, we would almost certainly buy a Ford S-Max Titanium. Even Jeremy Clarkson loves the S-Max. But no S-Max is available in the US, so an 2014 MDX is looking increasingly likely.
If we buy a 2014 MDX, we will almost certainly fuel it with regular gas. I was briefly back in the US (more specifically The Woodlands, TX) last week and I was shocked to see that premium gas now costs $.40 more than regular, a difference of more than 10%; regular gas costs slightly less than $3.50. I suspect that the oil companies are making a much higher profit on premium than regular because the demand for premium is not very elastic and stations typically advertise the price of regular making cost comparisons for premium more difficult. Oil companies understand consumer psychology well and exploit it when they can. Many of my friends work in the industry. (The Woodlands is a beautiful planned community built on the prosperity that flows from the oil and gas industry.) Next time that i have a chance, I will ask about the profit margin on regular vs. premium. Many, many people believe premium is much better than regular and worth the price differential, even when it is $.40 a gallon. In general, I don't. Unless I am filling up a car that absolutely needs premium (like the chipped 944 Turbo S Porsche that I owned two decades ago), I will use regular.
Here in Sweden, regular gas costs at least $8.15 a gallon. In Stockholm, $8.75 per gallon is typical. I generally don't look at the price of premium. Our 2006 Opel Zafira with a 2.2L DI engine (a GM Ecotec, ugh) runs on regular.