We originally started with Apache. We went that way because we did not have relationships with Eclipse Foundation, the Orion project - a perceived competitor at the time - was already there, and concerns over IBM having an outsized dominance / influence over the community.
When we reached out to the Apache foundation to discuss the ways we could get our software into their foundation, building mentors, and also cross-project collaboration - we really struggled. We were unable to get the necessary endorsements. Apache was really bare bones governance. Because we couldn't get the right mentors, the proposal never made it out of an early proposal phase.
Serendipity at the time had me accidentally meat the Orion project lead at the Eclipse Foundation. Conversations ensued, and a path for how Che could come to be a reality with the support of other vendors that wanted to get involved was laid out. And that lead to our ultimate path into Eclipse and promotion there.
So this is an interesting back story about how one project ended up in Eclipse vs. Apache.
Interestingly, Eclipse is opinionated about the projects they promote. They are topically focused and work for project cross-pollination along with driving marketing initatives and IP policies around driving adoption of their core underlying projects. So that is a bit of a departure from the Apache approach where each product is more autonomous in terms of its underlying promotion responsibilities.
This plays a little bit to @dr_faustus comment on Apache being a place where many large projects are going - they can do that because the community already exists and they need the most structured infrastructure / process.