Hamilton, chasing a 10th win of the year after wrapping up the championship in Mexico last month, lapped the floodlit Yas Marina circuit in one minute 37.877 seconds in the evening session.
"It's been a good Friday, but I'm happy that it's the last one of the season," said Hamilton.
"We got lots of laps in today and made good progress with the balance of the car. We have a bit of work to do, but I feel like we're quite competitive here. It's relatively close still, but I like that."
Vettel, who had set the pace in the afternoon with a lap of 1:39.006 and looked quick on long run pace, ended the day 0.149 slower and also expected a close battle in Saturday's qualifying.
The German is set to become the first non-Mercedes driver of the last four years to finish in the top two of the championship, leading Valtteri Bottas by 22 points into the final round. Both Hamilton and Vettel, a quadruple world champion with Red Bull, are three-time winners in Abu Dhabi although Ferrari have yet to triumph there.
Mercedes' British driver Lewis Hamilton steers his car during the second practice session as part of the Abu Dhabi Formula One Grand Prix at the Yas Marina circuit
Image credit: Getty Images
Red Bull were third in both sessions, with 20-year-old Dutch driver Max Verstappen taking that place in the first and Australian Daniel Ricciardo in the second.
Ferrari's Kimi Raikkonen and Mercedes' Bottas were fourth and fifth.
Brazilian veteran Felipe Massa, preparing for his last Formula One race with Williams, was 11th fastest.
"I didn't feel that anything was different or strange today compared with any other Friday, but maybe when we get to the first race of next season I will miss this, the competition, and everything else," Massa said.
"I'm ready for that and I think it's the right time."
The tight battle for sixth place in the constructors' championship between Toro Rosso, Renault and Haas -- with just six points separating the three teams -- is another focus for the weekend.
Nico Hulkenberg and Carlos Sainz were ninth and 13th respectively for Renault with Toro Rosso's Pierre Gasly 15th and the two Haas drivers Kevin Magnussen and Romain Grosjean 16th and 20th.
British youngster George Russell, taking part in first practice only, was 11th fastest in Esteban Ocon's Force India and less than a second off the pace of the team's Mexican driver Sergio Perez.
Russell also took part in first practice in Brazil, and looks set for a reserve role in future.
With both championships wrapped up, Mercedes having clinched their fourth successive constructors' title in Texas last month, most teams used the opening session as an early test for 2018.
Some also tried out the 'halo' head protection device that will be introduced next year.