There is no one best answer to your question without knowing more about how you intend to accumulate miles (flying? credit cards? purchase? exploiting promotions?), where you are located and where you are interested in flying, the time frame you are interested in accumulating, and so on.

For instance, when we're discussing the USA, US Airways has a better award chart for some areas of the world... but United's/Continental's has better redemption values for others, and their rules for changing tickets are more flexible than US's, plus United has one-way awards.

This statement is not correct.

List of *A airlines that do and don't charge fuel surcharges for awards

Please note that USA carriers as general practice do NOT charge fuel surcharges.

I would argue this statement is not necessarily correct, either, based on my own experience.

I've taken a grand total of two flights on US Airways since the beginning of 2010 (one was an IROP reroute/quasi-mileage run, one was a cheap LAX-LAS flight that I credited to CO- so only one flight, PHX-ORD where I credited to US).

I've accumulated around 200,000 US Dividend Miles during that time through various promotions- miles purchase, miles sharing bonuses, hotel point transfer, promotional participation, online shopping mall usage, and so on. I also don't primarily fly Star Alliance (my primary program for flying is Alaska Airlines), and the flying I've done since 2010 has largely been sent to CO Onepass. My accumulation has been enough to allow for a "mini-RTW" on US, and still leaving me with a healthy mileage balance for a future premium class award.

Many FTers use multiple programs for accumulation, since there are unique features to each one of them that can make them each useful in their own way.