I think you're confusing chuck eye steaks for ordinary chuck steaks.
Chuck eyes are more tender than your strip steaks.
Like what you like, if you are driven by price, fine. -- but I believe there is a world of difference between the strip and the chuck eye. From Fine Cooking
Strip
Top loin steak
Boneless:
strip steak, Kansas City
steak, New York strip
steak, ambassador steak,
veiny steak, hotel steak,
boneless club, and more
Bone-in:
New York strip loin, shell
steak, strip steak, club
steak, club sirloin steak,
Delmonico steak
Think of these popular steaks as
a T-bone or porterhouse with the
tenderloin section removed,
leaving you with the very tender
and juicy top loin muscle. May be
bone-in or boneless (shown).
Look for ample marbling. Ideal
thickness is 11/2 inches, giving you
a 3/4- to 1-lb. steak serving 2 to 3.
Chuck-eye
steak
boneless chuck fillet steak,
boneless steak, bottom
chuck, center-cut chuck
steak
This boneless steak, found under
the steer’s back bone closest to
the rib section, has good beefy
flavor and is relatively tender,
though it may also have a fair
amount of fat and gristle. Steaks
can weigh from 11/4 to 21/2 lb. and
serve 2 to 4
I'll go with "very tender
and juicy" against "relatively tender,
though it may also have a fair
amount of fat and gristle." Worth the price premium to me.