Alex once again has a very well-written blog post, but I disagree with it entirely. I could leave a really long comment or just write myself a new blog post. Andy Crouch took up the secular hope vs. spiritual hope compare & contrast and you picked it up, so I will add my thoughts (mostly restating Crouch, honestly.)
A secular hope is a great thing for educated people who have the resources to avoid most of the pain and insecurity that come with disease, hunger, war, and oppression. In fact, a sense of self-sufficiency and self-determination permeates most atheistic discourse that I really don't think can be extended to those who are suffering around the world. Even Steve Jobs, confronted by a horrific medical fate, was able to game the system in order to get a liver transplant that anyone in a similar situation in his part of the country wouldn't be able to get. The sad part is that this is only a mild example of the sort of injustice that allows the rich to live well at the expense of the poor across the world. To say to the billions of people who do suffer around the world and will continue to suffer until they die that we can have hope in this world really is a cold comfort.
I would argue further that a secular hope is not much of a hope at all, even to the educated and wealthy. Any part of life that gives us meaning can be taken from us at pretty much any time, no matter how hard we might try to protect it. Our health, our intelligence, our friends, our financial or physical security-- all of them are guaranteed not to last, and most of them will pass from our hands before we die. You can plan to die well and you can satisfy whatever meaning you've picked out for yourself before then, but it's still a crap shoot whether your kids will turn out alright, your work will be used for good, or your love will mean something to another person. And that's just in this life. If there is a world to come, then such a hope and the meaning we derive from it is laughably insignificant.
Furthermore, you can't know that the meaning you choose for yourself is truly... meaningful. We look with pity on, say, the people who died fighting to preserve slavery or the Tuskegee researchers, but we can't know if perhaps our choices will be just as harmful to others. Lots of people, regardless of class or religious preference, choose terrible meanings for themselves to actualize, most of which are oblivious to the needs of others or contravening them entirely. You say, "Which is the better source of hope: this world, small, and often backwards as it is, but certain, or transcendent meaning and eternal life, known by invisible evidence? What can comfort?" I would argue that the hope of this world is not in any way certain and it is the security & comfort that we have bought for ourselves that deceives us into that certainty.
Now, turning to spiritual hope. I don't think that you can have hope without faith. After all, on a superficial level, hope is simply wanting something good or better to happen in the future. Like buying a lottery ticket. No one is going to buy a house beyond their means expecting to pay it off when they hit the mega millions. But if you've got hope that isn't just what you want to happen, but something that will happen-- then that's the sort of hope will motivate you and give you security. You might buy a house beyond your current means if you know your trust fund will start paying out in 6 months. So a truly substantial hope will lead to truly substantial things. A temporal, worldly hope is always tenuous, because you can never actually give yourself to it with reckless abandon. Yet spiritual hope allows you to give yourself to others, to pour yourself out in love knowing that even if you lose everything else, you have the treasures of heaven. This hope is born out of faith grounded in what we can see & feel but not limited by it. Secular hope is a like buying a lottery ticket in the expectation you'll hit it big; spiritual hope is like being adopted by a rich man with a huge trust fund in Switzerland knowing that you'll get it the day you turn 21. Even if you can never see the millions, you have his constant reassurance and testimony in the past and today that he's taking care of you.
Starting from the Resurrection of Jesus, we see God showing us that we can have a true hope. Jesus, the firstborn from the dead, gives us a meaning that is far more powerful and beautiful than anything we can come up with ourselves. Anything else is like buying the lottery ticket: false hope that's a waste now and foolish in the light of eternity.