There are any number of empirically-supported surveys of car reliability, Consumer Reports being the most obvious. I'm not American but I can understand the desire to buy from a company based in one's country. But it is pretty objective that the Japanese brands have long been more reliable than their competitors. As others have pointed out, recent gains by the US manufacturers are laudable, but not relevant for Mustacheans buying 8-10-year old cars. For that vintage, the stats are simply that Toyota and Honda are more reliable, on average, than other makes.
People freak out about statements like this, but I don't really understand why. It's fairly widely-agreed that German cars are more expensive and less reliable than Japanese, but the 'defenders' of these brands generally cite the driving dynamics as being worth the cost. What I don't get are people who are supporters of the Big 3 not using similar logic - e.g. An Impala, all things being equal, will probably be less reliable than a Camry. However, the purchase cost is less and you have the satisfaction of of buying American. Plus, you might happen to like it better simply due to personal taste. That seems to be a better reason than, "My uncle had one go half a million miles and I heard Toyota had a recall, so you must be wrong about your views of American cars". Put another way, if someone told me that my car was less reliable than theirs or X brand, my response would be, "yes, and I still like it better." Not sure why it becomes a personal affront to one's nationality or a perceived insult to one's judgment or intelligence.
OP, rather than rely on most of us, who by very nature will give you anecdotal responses, hit the Consumer Reports and JD Powers of the internet. There are plenty of valid criticisms of both, but statistical surveys are better than the proverbial water-cooler. If it were me, I'd pretty much stick to Corolla/Camry or Civic/Accord if your criteria are reliability, fuel economy and that is based on the services noted above.