The AA Route Planner advice is go via Hastings and Rye:-
From: Newhaven,East Sussex
To: Channel Tunnel,Kent
Distance: 70.2 miles
Time: 1 hr 41 min
Via the M23 etc:-
From: Newhaven,East Sussex
Via: M23
To: Channel Tunnel,Kent
Distance: 108.1 miles
Time: 1 hr 55 min
I guess the difference is whether you prefer your average speed to be 41.7 mph, via Rye, or 56.4 mph, via the motorways, with an extra 37.9 miles thrown in.