It's complicated. From her lines, Essex appears to look up to Enterprise, but also feels a need to surpass her.
I don't think it's that complicated. Yes, Essex has mixed feelings about Enterprise, but she doesn't view her with animosity at all-- her rivalry is nothing like the one between South Dakota and Washington, or Akagi and Shoukaku. The "Essex is tsuntsun for Enterprise" thing only started after the Bilbury animé, where it gave people an excuse to start 'shipping Enty with Belfast.
This...is pure blasphemy against the sacred order of fish and chips.
It's karaage, though. Sometimes a bit of lemon is squeezed on it, but some people don't like it, and Enty and her tiny self doesn't like lemons, and Essex gave her more than a little bit.
