Let's put the question simplier:
Which is best for:
- quick pictures/sounds loading and presentation
- accurate stopwatch timing
- overall speed of processing
Thanks again !
You are asking the wrong question.
What you should consider is install-base, features and costs.
Unity is by far the easiest option to use as it is a complete game engine, it doesn't have a browser plugin for Linux (you can build downloadable linux games though) but Win and Mac users will be able to play your game just fine. The free version has some graphical limitations (irrelevant for 2D games but for 3D they can be a problem), the pro version costs $1500 per seat, not all users have the plugin installed and some may be unwilling to install it just to play your game.
Java is quite a bit harder to use and for advanced 3D graphics you will have to digitally sign your applet (in order to use native libraries such as LWJGL), it works on pretty much all operating systems (including less popular ones such as BSD and Solaris) but some users don't have it installed and may be unwilling to install it in order to play your game.
And finally we got Flash, it is installed on some 90+% of all desktops allready so most users won't have to install a new plugin, allthough not all users will have the latest version(so if you want to use 3D graphics those users might have to update their plugin), works on Win/Mac/Linux(Allthough adobe no longer updates the linux plugin with new features, just security updates so the latest version there is 11.2, for Win/Mac its 11.8), performance-wise its a bit behind Java and Unity but unless you do very heavy processing it is not relevant. (Older flash versions (8 and older IIRC) are significantly slower though)
Thus my recommendations:
For 2D games, go with Flash or Unity (Unity can be slightly easier to use(depending a bit on the game) but more users have the flash plugin allready installed)
For 3D games go with Unity or Flash. (Unity is a lot easier to use for 3D but you won't get things like dynamic shadows or effects that require render to texture with the free version)
For very advanced 3D games go with Java or Unity pro.