What are the big differences between TFS and Git for source control when using VS 2013?

MSDN has a very extensive page on all the features and differences between Team Foundation Version Control and Git.

Is the only benefit in my case a local repository (not saying that's insignificant) and IoS development support?

No, there's lot more, but they're often advanced scenario's of Git. Local Repo, offline support and full local fidelity on history is incredibly powerful, you get that out of the box with Visual Studio. There's a few other features that are great too! The ability to branch and merge from one repository to another is very powerful. I recommend you look up the Pro Git book for those. Git in TFS is just another git server, it has pretty much all features that the standard Git has.

The ability to rewrite history before merging allows you to remove or combine a number of smaller change sets, so that the history is cleaner and easier to read as a human.

Is the only drawback to Git the command line interface (some would argue that's not a drawback ;-P).

TFVC has a command line too, people just don't use it. For people that want to use Git and never do much more than TFVC does, they probably won't really need to leave the UI, they won't get a lot of the cool features though...

There might be a few other drawbacks, mostly due to the fact that it's different than what people are used to. It's not too hard to shoot yourself in the foot if you don't take the time to learn what git does when you do things. Things like Rebase and Squash are really powerful and create a very clean history, but it can leave people with the problem that they can't merge anymore if used incorrectly. TFS has the ability to put some security settings to take away the rights to make very stupid decisions on a git repository.

A very cool add-on for Git users on Windows is PoSHGit. it provides command autocompletion on the Powershell commandline.

Have you experienced in the VS 2013 GUI for Git? Is that enough to support basic branching/merging without the command line interface?

It has all you need for basic operations. But you do need to be able to visualize the different branches to know what's going on. Since the Git server and local repo are just Git, any git client can help you out here. SourceTree is an option here. The Git for Windows client is another.

For standard operations, check-in, check-out, merge, branch (or push, pull, fetch, commit, merge) the UI works just fine.

Is there a detailed start-up guide for Git that shows Git being used with VS 2013? MS has a video for integrating an existing Git repo into VS 2013, but I'm looking for a start from scratch with Git and VS 2013?

Starting with Git is available in a number of places... These are a few options:

Other good reads:

And a few tools worth installing: