Bootstrap is awesome for people who aren't comfortable with CSS and just want to put up something quick and don't mind if it looks like every other site out there.
Foundation lets you write better markup.
Also, If I remember correctly... Bootstrap has caught up now, but in earlier versions, their grid wasn't nestable, which made it almost useless for sufficiently complex websites.
Bootstrap's eco system is huge. If I had to use one, it would be Bootstrap. Since I can choose either, I use Bootstrap most of the time and Foundation when I need more control.
For the variable parts, thats another myth: you can override variables easily.
I have nothing against Foundation, but to me, all the frameworks claim silly things to gain developers and developers aren't that kind of stupid consumer.
Just bring the facts, let the devs decide.
There is also a smaller community around Foundation, which is good and bad: there isn't the massive third party ecosystem that Bootstrap has [1] but on the flip side many feel that Foundation sites don't look so 'Bootstrappy'.
I'm really invested in Bootstrap, but I'm stoked that more and more people are using front-end frameworks as they pretty much across the board improve developer productivity and make sites better/more usable.
1 - http://www.bootstraphero.com/the-big-badass-list-of-twitter-...
However, I think there is some massive confirmation bias at work. If a site customizes Bootstrap and it looks nice nobody credits it as a 'Bootstrap Looking' site, so as a result it is only when the defaults are used that people really pick up on it.
That coupled with the fact that there are many more Bootstrap sites kicking around out there I think has led to the misconception about "Bootstrap Looking" sites.
Bootstrap is more like a theme to me, if you don't want to bother buying one and you don't mind having a "bootstrap" look go for it. I love doing quick mockup with it. But as soon as you have to design something, it's a trap, it makes you lazy and want to use their styles for everything.
Foundation has a better reset in my opinion (I like box-sizing:border-box). The rows act like a container (size depending of your configs) whereas you can play with row and row-fluid in bootstrap (which might not be a good idea on a project). Also Compass + Sass. Forms look better. Orbit looks better than Carousel...
These past weeks I've been using both since I can't really make up my mind on one. I'm going to dig into Foundation 4 to see if it's going to change the situation.
EDIT : I'm looking at it right now, it does look pretty awesome. It seems they're taking a very different direction from bootstrap: - you now have to stylize elements through CSS (or SCSS) like it's supposed to be! They provide a long list of example, it seems like their stuff is entirely and easily customizable (which was always the shortcoming of Bootstrap). - I taught a friend who didn't know HTML nor CSS how to make websites a few day ago. I taught him Bootstrap. He's loving it since then. Looking through Foundation 4 the idea that it would be way too difficult to teach him Foundation 4 has stroke me.
Personally, my main reason for using Foundation over Bootstrap is that it's not Bootstrap, meaning for side projects and demo sites I can leave the default styles without people complaining about "another Bootstrap site".
For example, I launched http://toogl.es recently on Foundation and it gets a lot of developer or other technical users.
With Foundation, it is much easier to override their styling and build something that is unique. You feel more like you are working WITH a framework, as opposed to working AGAINST one - which is how I feel using Bootstrap.
Either way, you can't go wrong, but if you value saving time by not overriding a million CSS rules when designing your site - go with Foundation.
My take is that Bootstrap provides a lot of stuff out of the box (including a rich third-party ecosystem) but Foundation is better suited as a customizable, well, foundation for your site.
Apps using Bootstrap benefit from the larger community of 3rd party controls and libraries and, why not, from a consistent UI look that I don't have to mess with (no, I don't mind that my buttons look like everyone else's, I quite enjoy it actually).
Sites using Foundation benefit more from the mobile-first approach (Bootstrap is indeed catching up to this) and from easier customization (SCSS) and blander default styles, leading to a more distinctive look.