The main train operator serving Brighton, Hove and Portslade has the lowest rate of customer complaints outside London.
The rate for July, August and September – the second quarter of 2013-14 – compares with five complaints per 100,000 passenger journeys in the same quarter a year earlier.
Only London Overground had a better rate with two complaints per 100,000 passenger journeys.
The ORR said that the rate for First Capital Connect had dropped from 18 complaints per 100,000 passenger journeys in the second quarter last year to 16 this year.
The regulator published the figures yesterday (Thursday 19 December).
The BBC reported today (Friday 20 December) that Southern paid passengers £805,000 in compensation for delays in 2012-13.
First Capital Connect, which operates the Thameslink route from Brighton, paid out £722,000 in 2012-13 – an increase of £85,000 on the previous year.
According to the BBC, the company blamed Network Rail, which owns the infrastructure such as tracks and stations.
The payments were made under the Delay Repay scheme for passengers whose journeys are delayed by more than 30 minutes.
If a passenger is delayed by between half an hour and an hour, he or she is entitled to compensation worth 50 per cent of the relevant single fare.
If a passenger is delayed by more than an hour, he or she is entitled to compensation worth the price of a single ticket or half the price of a return fare.
Southern was reported to have said that growing awareness of the scheme had led to a rise in the number of claims.
First Capital Connect was reported to have blamed Network Rail for more than half the delays.
Network Rail said that it was investing in longer platforms and new signalling on the network, according to the BBC.