We're starting to recommend Drupal 8 for some new upgrade projects, with the following notes...
Because Drupal tends to be used by sites that have pretty complex data structures, major upgrades can be painful. We basically build the site in the new version, and migrate the data into it. Drupal 7 has a migration tool that helps pull the data over, but we need to first create each content type and field, and then map it to the data in your current system. Once that's done, the big advantage is we can run it alongside the current site while making improvements, and easily grab any new content as it's created in the old site.
Drupal 8 does save one step -- this migration system is built into core, and it's capable of auto-creating the data structures for us (currently from Drupal 6 or 7, not from 5). So that can save a lot of setup of the data structures on the site. It also has a completely re-vamped code architecture under the hood that promises to eliminate (or at least greatly reduce) the pain of future major upgrades -- it should be possible to upgrade small parts of the site individually, one at a time, instead of it being an all-or-nothing complete site rebuild. So if we can migrate to Drupal 8, you're getting most likely a minimum of another decade before you have to completely redo your site -- and possibly a lot longer than that. With Drupal 7, you're getting something that will still need a major rebuild to get to Drupal 8 (or 9) probably 3 - 5 years down the road.
The question is, is Drupal 8 ready yet for your needs? At this writing it's currently in Beta. It has in the neighborhood of ~50 critical issues that need to be resolved before it is released -- in our estimation, there's really only one complete showstopper in there, and that has to do with upgrading between betas and the "release candidate" and stable phases. Once we know there's going to be a supported minor upgrade path, we think everything else can be cleaned up as we go.
And that's not a showstopper for doing the upgrade -- just for actual launch. Given that it takes generally 3 - 8 weeks to do a new site, we could start that now, dial in the theme and the migrations, and assuming this issue is resolved by the time we're ready to launch, we update to the latest beta, run the migration from your current site, and launch.
Drupal 8 also has a lot of mobile-targeted UI right out of the box, it's a great mobile experience without any work at all.
All that said, there's definitely a risk that you'll want to launch before that's ready -- if you'd prefer to have a more straightforward, less risky timeline, we still do lots of Drupal 7, and everything mobile-friendly these days!