The capital’s council-owned main bus operator scored higher than or the same as the FirstGroup-owned firm in all 34 categories of the survey.
However, more than nine in ten passengers were satisfied overall with both operators - 96 per cent with Lothian and 91 per cent with First.
Lothian’s figure was also higher than all 34 English operators surveyed in the report.
Passenger Focus chairman Colin Foxall said: “Lothian Buses scored outstandingly for overall satisfaction and value for money ratings, while First Glasgow also scored very well.”
Lothian passengers’ satisfaction with value-for-money was 8 percentage points higher than First’s, at 79 per cent, and satisfaction with punctuality was 7 percentage points higher at 91 per cent.
However, the biggest difference between the operators was the cleanliness of the inside of buses, with 88 per cent of Lothian’s passengers happy - 11 percentage points more than First’s.
Lothian also scored ten points better on the condition of the outside of buses, at 90 per cent, and nine points better on seat comfort, at 87 per cent.
The survey, of more than 2,000 passengers in Edinburgh and more than 3,000 in Glasgow, was carried out between last September and December.
Passenger Focus included the two companies for the first time in its survey of English operators which has been running for four years.
Both paid to be included by funding the research, but the watchdog said it was carried out with “exactly the same rigour” and did not affect the results.
Glasgow Green Party MSP Patrick Harvie, who founded the Better Buses campaign in the city, repeated his call for greater control of bus services to force improvements.
He said: “It’s to be welcomed that passenger satisfaction was high across the board. But there’s a significant gap in satisfaction and value for money between the main providers in Glasgow and Edinburgh.
“If we want to encourage more people to make the shift to public transport, we have to be offering an outstanding level of service.
“If the market can’t deliver the same level of service as public ownership, then the Scottish Government should be looking at ways to bring it up to speed.
“I will continue to support calls for Scotland’s local bus services to be re-regulated.”
The Passenger Focus results contrast starkly with a poll by the Better Bus campaign in 2012, which found two in three passengers thought buses in Glasgow were unreliable and more than half had complained about services. Three in four did not view fares as good value for money. First questioned the accuracy of the findings.
Lothian Buses chief executive Ian Craig said: “Knowing that the vast majority of our passengers are satisfied with all aspects of our service is excellent news and shows the outstanding levels of service that our staff are continuing to provide.”
“The fact that we have topped the survey is even more encouraging and reflects the efforts our team make across the business to provide the best possible fleet and services.”
First Glasgow managing director Fiona Kerr said: “I’m delighted with these results. They reflect the commitment, determination and capital we’ve invested over the last 12 months to improve services for our customers.
“We’ve launched a brand new network, simpliCITY, which is performing well and providing customers with better and more frequent bus services, we’ve invested £24m in 151 brand new vehicles; and we are delivering services that are more punctual and reliable.”
Passenger Focus acting chief executive David Sidebottom said: “Lothian Buses can really be proud of these results, particularly with the very high level of passengers’ overall satisfaction.
“These results show what can be achieved if bus passengers are provided with a punctual, reliable, and value for money service on clean and comfortable buses.
“Lothian Buses is one of many bus companies, so we hope other operators recognise the potential value of working with us to find out what their passengers really think of their buses and then take actions to improve passengers’ journeys.”
Buses magazine editor Alan Millar said: “Lothian is a very well-run operation, maybe helped because it is focused entirely on Edinburgh and environs.
“It also has a stable management team, which until recently wasn’t a feature of First anywhere, Glasgow included. That has now changed.
“While I am sure First Glasgow is now getting its act together, First’s past performance was poor and it has a huge amount of catching up to do to match Lothian’s standards.”