score:4
The morning option is much better, there's more trains and you can go direct to Elephant and Castle without needing to change trains.
Useful resources:
TfL journey planner: https://tfl.gov.uk/plan-a-journey/
Thameslink train timetable: http://www.thameslinkrailway.com/download/11029.2/b-all-thameslink-services/
By 8am you're right in the middle of the morning peak and everything should be running - but in the middle of the night it goes down to only 2 trains an hour from Luton Airport to London, and that train doesn't take you all the way to the Elephant. Go for the morning one.
Also, you can check in advance for scheduled engineering work here: http://www.thameslinkrailway.com/your-journey/engineering/
You have to get a bus from Luton airport to the railway station, it costs Β£2 and is cash only. Takes about 10 mins. http://www.london-luton.co.uk/to-and-from-lla/travelling-from-london-or-the-south