Not necessarily. Studio Ghibli's headline achievement would likely be considered to be Spirited Away (although I prefer Princess Mononoke), which is nearly as old, but they've still put out some solid work since then.
As dragontamer pointed out, Gainax has also produced Gurren Lagann in 2007, which is definitely a pretty big hit, even if it wasn't the phenomenal success of Evangelion.
Gurren Lagann is rated #1 series of all time by many anime fan, myself included. It's a masterpiece, although the cultural impact isn't of the same level as Evangelion.
Seconded on Princess Mononoke. TBH, I haven't really enjoyed any of Ghibli's modern stuff since they moved from stories with morals to essentially dream sequences.
That’s Ghibli though. The company that somehow can do Disney style mass appeal and contemplative art films, often at the same time.
Gainax makes fantastic, often quite out there, shows that play with anime tropes. Their addressable market is people who are already at least somewhat anime fans.
As dragontamer pointed out, Gainax has also produced Gurren Lagann in 2007, which is definitely a pretty big hit, even if it wasn't the phenomenal success of Evangelion.