I tried compressed plain SVG (.svgz), the files are smaller and it looks the same than the regular .svg. Is there any downside? Can I use always .svgz?
.svgz are simply gzipped svg files. The only caveat in their use is that the web-server delivering them has gzip enabled and is able to correctly set gzip headers.
All (well IE8+!) browsers support the format itself
We're venturing into stackoverflow territory here, but enabling gzip on your server is likely as easy as pasting this into .htaccess:
PS - Also check out SVG scrubber which is very cool.