The title of the thread asks which is more punishing while the poll asks which is a worse fate. I would say that life in prison is more punishing but death is the worse fate. Why death is a worse fate is obvious--it's the ultimate end, after that it's all over. But it's not always necessarily more punishing. Bullet to the head, lethal injection, whatever, in either case it's over in a relatively short amount of time (assuming nothing cruel and unusual). Not to mention that death is something we all inevitably face--the death sentence merely accelerates when that happens.
Life in prison on the other hand is more punishing because it lasts for the rest of your life and the only thing to look forward to at the end is...well death. So on top of the life in prison, you still also get death at the end. Your time is limited, but you're severely limited in what you can do with it. Being stuck in a building full of rapists and murderers can't be fun, let alone being in that environment for the rest of your life.
But it does have an upside, which is the possibility for the person to (eventually) see and fully appreciate the consequences of their actions and with time actually become remorseful. Some people do stuff when they're young and to them death is just a word, the gravity of what that really means doesn't fully click--heck in some cases they might even prefer it (many criminals who go on killing sprees try to off themselves before they're caught). But over time and seeing what their legacy is, as they get old they can serve as a living warning for future potential criminals (like that show "Beyond Scared Straight"). The criminal becoming remorseful can also help bring closure and healing for the victims/victims family--not that the criminal gets released or anything of course, they have to live with what they did. But they can help the victims understand why it happened, which can be helpful for some people.
Not to mention the fact that it's also a potential source of affordable labor. At least with that they're able to make some positive contributions to society--which can potentially make up for the cost of their living expenses (as opposed to how expensive it can be to have someone executed).
There's also always the possibility, however slim, of some new evidence proving the innocence of the person years or decades later (rare but it has and does happen). Wasting 10-20 years of a person's life is much better than saying "oops, we executed him by mistake".
So overall I think life in prison is both more punishing and more productive/beneficial. But death is the worse fate.