From memory, I think the Equinox was an old design dusted off, but it was for what eventually became the Defiant.
Edit: Thanks to Memory Alpha:
"I was searching through piles of drawings for little ships just to get some inspiration and I came across a sketch that I had done for the Deep Space Nine Tech Manual of the original design for the USS Defiant before... [it] was given all of its armor and upgraded weapons, what we call the Pathfinder vehicle... and I thought, 'Well, we haven't seen this one yet, so maybe this design could turn into the Equinox and the drawing was approved and we fleshed out the Equinox for the two-parter." -- Rick Sternbach