Blimey what part of it do you use? I've found them to be the worst London area TOC. Mainly due to their very poor communications in times of trouble. For example they were the last to get an active twitter account after all other TOC had realised its value to commuters, and they also suffer from very poor communications at many stations when problems arise. Never used connex but communications are worse than under their directly operated predecessor.
How many southeastern trains will be freed up by services moving over to the new TSGN franchise up to 2018?
When I first started commuting to London in around 2003-2004 (I think) the 25 min journey from Orpington to London Bridge used to take 40-50 mins an average of 1 time in 5, with the rest being 30+ mins.
I can't be sure but I think Connex were still in charge back then, or had only recently lost it.
by the time I moved office about 2 years later journeys of longer than 30 mins on that service were the exception.
Since then I've used Orpington-> Teddington via Waterloo(E) [SWT was good but I was going against peak],
Orpington -> Vauxhall via both Waterloo(E) and Victoria
And most recently ( up until April this year) St Mary Cray -> Vauxhall
I found all of these services to be reasonably reliable and most of the time not more than a few mins late.
I do agree however that communication is poor.
Having said that I believe recovery time to be better than other TOCs (though I have no evidence for that - it is based purely on personal observation)
These days I have to suffer the combined First/Southeastern service from St Mary Cray to Blackfriars.
A service I have found to be slow and unreliable. And it seems to be getting worse too (recent weather aside)
At the slightest hint of major trouble the default solution seems to be to cancel everything (ok if the problem is in the core I can partly understand this - but outside no excuse) turn trains around early, or skip stops used by the majority of passengers.
I do recognise that this is all based on personal experience only - not on any official stats of any kind, so maybe I have just had an unusual run of luck that doesn't tie in with most peoples experiences.