The case of editors/IDEs is a little different as there are a large number of genuine competitors. In the case of TeX distributions, on the other hand, the choices are much more limited:
- GNU/Linux, Mac OS X, Windows, the BSDs... If it isn't available out-of-the-box for your OS, you can download the sources and probably get it working. But for almost everyone, pre-compiled binaries are available.
- No. (But if possible, it is best to have admin privileges to set up a specific location and user. However, it is recommended not to install with admin privileges.)
tlmgr (in between releases); new installation (to update to a newer release).
tlmgr, cross-platform, excellent support, very well maintained, extremely active community.
- A portable installation can be installed on a USB key.
This is just TeX Live for Mac OS X. It does, however, require admin privileges to install. (But you can change this afterwards so updates don't require it.)
- Has built-in facilities for ongoing updates. New releases may require new installation.
- On-the-fly installation of packages required during compilation; not cross-platform.
TeX Portal, TeX Writer, TeX Pad etc. are specialised distributions, generally smaller and sometimes minimal, for specific needs e.g. for use on mobile devices.
ShareLaTeX, writeLaTeX etc. are online distributions where you compile using a distribution installed on the site's servers.
For installation on a desktop or laptop, you almost certainly want TeX Live or MiKTeX unless you are happy to rely on online options (e.g. if you don't use TeX often or are just trying it out).