Microsoft Office is not free. OpenOffice is free but really slow. IBM Lotus Symphony is free but really slow.
What's the solution? EDIT: Is there any fast and free office suite?
You're making some sweeping generalisations about complex pieces of software, so here are some sweeping generalisations of my own...
Microsoft Office is heavily optimised for Windows and was developed with the extensive resources available to Microsoft. The free suites are less optimised for a particular platform and are arguably less mature products, but the features are good and the price is great.
If you want the best of both worlds in this particular case, you'll need to pay for Microsoft Office or pay for faster hardware to run the free suites.
I would also recommend LibreOffice. It has all the features of OpenOffice, but shows significant improvements and was also reported to be quicker.
Otherwise, on linux you can try so called Gnome Office, which is (I think) combination of Abiword, Gnumeric etc. For me it was not the right choice, so I use LibreOffice.
KDE also has something, but never used ...
OpenOffice is now in the hands of the Apache Foundation, before that Oracle pretty much ended development.
LibreOffice is its replacement, basically OpenOffice has been forked into LibreOffice:
Depending on your needs, you may not need an office suite, both Microsoft and Google have web based office applications:
Office Web Apps: http://skydrive.live.com/
Google Docs: http://docs.google.com/