The best way, regardless of what time of day, or what the crowds are doing, is via the ASIA entrance.
Why?
A. Because it is a SHORTER ROUTE to the ENTRANCE to EE than going via Dinoland entrance.
B. Because if the crowds are building the lines, you will have to WALK PAST them to actually get IN the line, if you come in from the Dinoland direction.
Like many "routes" at WDW the one you come to "FIRST" is not necessarily the one to choose... because of the convoluted direction it may follow.
Dispite how it may appear just LOOKING at it, the route through Dinoland is quite a bit LONGER in distance than the Asia route. Enough that if the crowds are pouring in, you'll end up much farther back in the line by the time you reach the queue.
And, if you are there in the morning for Rope Drop, a CM will walk you (and hundreds of your closest friends) back to EE anyway (via the Asia route).