First of all, I would never choose svn. There might be some cases, but in general git is much more flexible.
That said, let's look into Continous Delivery (CD). From my point of view, this means to deploy often. It also means you need some kind of Continous Integration (CI) where you run your tests and decide if the version gets shipped or not. It also means you need some kind of workflow on how to determine which version gets tested and shipped.
Back in the svn days, we didn't have any branches because it was to troubling. Everyone would commit into the repository and then someone responsible for shipping would see if everything is ok and use his version of the repository to ship.
This is cleary not going to work with CD because you wantat least one stable branch. This branch should only be populated with stable releases of the software which then gets into production. You also want a testing branch where features get merged that are ready to be tested and then deployed. And you want any number of development branches, where not-ready-yet features are located.
Make no mistake: You can do CD with svn. It's just that git was designed to work well with many branches and remote repositories on different servers while svn was designed to work as a single repository where everybody can commit to.
You also might get a problem with user management. I don't know about svn, but I think you can not have different rights for different branches. This means that everyone with write access to the repo can break your application and have this stuff deployed. On the other hand it's easy to set up a repository where only a senior developer have write access and which gets deployed. All other developers work on another remote repository. The person in charge then pulls all the stuff and pushes them to the other server so they get deployed.
This all comes from the fact that git was designed to have many repositories which get merged together, branched, forked and patched on a regular basis (open source projects). On the other hand, svn is more of a company software where you need to version your files and maybe have a branch or two for different versions of your software, but not much more.
Last thing: I would choose git over svn every single day.