...should I delete it (which Matt Cutts suggests in one of his early videos about Panda) or do a permanent redirect to the homepage (to pass the link juice)?
You definitely should not redirect to the home page, unless the home page would be relevant (and it doesn't sound from your comments that it would be).
Possibly, you could redirect to a relevant category page, but again, if the traffic that has been coming is seeking a discontinued service for which there is no equivalent, then a relevant and satisfactory category page is likely to be hard to find.
IMO, if you're not going to rewrite the page, it's better to have it turn into a 404 (perhaps with a welcoming custom 404 error page) than to have disappointed searchers come to your site and back out.
If your site has a lot of churn like this, though, you should consider ways of rewriting the outdated posts to give visitors choices... ie, additional text description and links to other pages on your site that might apply.
If, eg, this service that you reviewed has been shut down with no alternative, that in itself might be useful information to searchers... particularly if you can find somewhere useful to send them, so searchers aren't simply backing out and searching again.