I have both a Git and a git-svn remote - and experience problems!

It's important not to have a Git remote and a git-svn remote with the same name. If both Git and git-svn have the same remote name, the remote branches of the remotes will overwrite each other; and there will probably be other side effects, too.

git-svn remotes do not show up in “git remote -v”, as their config is different:

[svn-remote "svn"]
    url = https://host/svnrepo
    fetch = trunk:refs/remotes/svn/trunk
    branches = branches/*:refs/remotes/svn/*
    tags = tags/*:refs/remotes/svn/tags/*
[remote "origin"]
    url = https://host/gitrepo.git
    fetch = +refs/heads/*:refs/remotes/origin/*

Tower, however, displays git-svn remotes as normal remotes.

If you need to have both a Git and a svn-remote, you should clone the svn remote with “--prefix=svn/”.
For some reason, the git-svn team chose “origin” to be the default prefix name; this can be problematic as you cannot have a Git remote with name “svn” nor “origin” as they would collide. If you use the prefix with “svn/”, you can then add your Git remote as “origin”.