Answering the opening question: This is because the web browser, whichever you chose, is more capable than any other application you have.
The web browser is an application that can run other applications and it's much like an operating system itself (and everyday more). And the specifications for building these web pages and "web apps", aka the web standards, are ever improving and receiving new functions so developers can build even more complex web apps/pages. Outlook.com and GMail today are not like Hotmail and GMail from 10 years ago (pre-Opera9), they're much more feature-rich, use caching for messages, have better performance and smoothness, animations, decreased full page reloads through intensive use of JavaScript, etc. The browsers evolved and use more resources to be able to deal with that and offer all these features to web developers.
I didn't experience this slowness you're describing in Opera 9~11. But in Opera 12+ it started to handle plug-ins differently so you may have a problem with that, this might be a source of a memory leak. On top of that pages are much more complex now and Presto isn't able to deal with them anymore, this is independent of RAM usage.
You should try Opera 24 (Chromium-based, changed everything: engine, handle of pug-ins, multiprocess architecture, user interface, etc). Independent of RAM usage (either more or less being utilized) you'll see the better performance.