HI Richard,
Welcome to the club. I think Michael said it best: New the Essence is ~$6000., but the Eagle is $1600. How can those 2 compare? THE BEST way to compare these 2 guitars is through an amp! That's where the Alembic shines! I owned an Eagle just before I got my Alembic Series 1 WAYYY back. I never went back! I liked the build quality of the BC Rich neck-thru, and it played great. BUT, I quickly tired of the one or two sounds the Dimarzio electronics could do. It's only good for loud rock. If you want versatility and MANY sounds, don't wait a second longer and buy the Alembic! The Essence has a low pass filter with fixed Q, and even though this is a simple circuit, it will blow the BC Rich away. You will NEVER tire of the Alembic total package: Feel, sound, versatility = synergystic balance! IF you go for the Rich, you will find yourself saying: It's nice, but it's NOT an ALEMBIC!
Good Luck!
Kris