We use visual studio team services(previously visual studio online) for all our projects. The main pro is integration with all other MS stuff(something you expect as a MS-based dev).
MS has also been working hard into making it usable with a Git repository instead of TFVC, in fact, there's a lot of features and workflows that only work with Git - e.g. branch for work item, pull requests, etc(I'm debating switching from TFVC to Git because of this).
It has a lot of the features you'd expect from an issue tracker - projects, teams, kanban boards, iterations, a dashboard, the "work item" with all its configurable fields.. since it uses TFS as a backend, there's also the awesome query builder which gives you tons of ways to create queries and filters to dig into your work items - this is probably great for management. There's also a very complex permissions system(I assume, again using the TFS backend).
The main con for me however is the abysmal UI around discussions on work items. The discussion by default is stuck in a tiny part of the already cluttered work item screen(this has changed recently as they introduced the ability to fully customize the layout). There's a single textbox with a "smart editor"(ugh) where you can type your comment, and some limited hyperlinking(you can address team members and link work items), and you need to press "save"(which is actually under the default option "save and close") for the work item to add your comment. It's pretty clunky to monitor conversations(email notifications) vs github's notification hub.
Oh, and they're a bit light on various smaller features, but they've been churning out new updates constantly, so I think they'll catch up.
As a top-down, management-heavy approach, TSVS is probably a fine system. As a collaborative workspace for a small dev team with very little management, I find it lacking the killer feature of rich discussions that Github has.
[1] https://www.visualstudio.com/team-services/