Best/Worst
Now that we've answered one of the questions, I'll take a stab at answering the other:
I think that you can obtain a good idea of the worst by perusing the pages of PPRuNe and reading the threads - especially those which have been going on for some time and have enough responses to be meaningful (a thread with two or three responses criticising a company is probably not as indicative as one with hundreds joining in and adding to the conflagration.)
Based upon this, by virtue of number of responses in relation to size of the company and the virulence of the debate, I nominate Prestige Jet as a candidate for Worst Company. EK, EY, QR and others have their issues and detractors, but nothing comes close to Prestige Jet in respect of the nature of this issues - that thread has everything from non-payment of salaries and expenses, seizure and repossession of jets on trips, passengers being asked for money to pay for fuel, pilots who ask for their pay being framed and accused of crimes, money laundering, ripping off a customer for $5 million, shady characters visiting captains with envelopes of cash on the streets of Riyadh and Amman, bribery of GCAA officials with cash, trips and women, unsafe operations, having prostitutes on board for the amusement of the CEO, CEO and Managing Director brother in hiding in Jordan, and a Chairman - Sheikh Hamed Bin Hamed - who is a member of the Royal Family of Abu Dhabi yet does not pay his employees and ignores judgments and orders of the Courts of Abu Dhabi to pay his employees and former employees who have won judgments against the company.
And, if that's not entertaining enough, the CEO and surrogates consistently coming onto PPRuNe in order to spew a stream of invectives at their own employess - and indicting themselves for mismanagement, incompetence and corruption, in the process.
It's a made-for-TV-movie in the making. Compared to that, the complaints about the major carriers seem mundane.