I was recommended these two languages as a good option for multiplayer web game development, but I don't know what are restrictions of these languages in terms of game development. I personally like JavaScript, but I'm not sure about client-server communication and security.
Game is going to be 2D turn based strategy.
Shortest answer: Flash.
Short answer: Flash is your best option at the moment, but it's entirely possible to make a good quality game with javascript, there's libraries out there that make the drawing part really easy.
Long answer: For action heavy games, such as a fast paced platformer or a fighting game, Flash is your best option. Flash is also the only option if you want to be able to sell your game to various portals, since they have not yet opened up the ability to license HTML5/Javascript games.
However, Javascript is a viable game development language. Angry Birds on Google+ (and in the chrome store) uses Javascript, and only uses Flash for audio. In fact, audio is currently the biggest challenge, and there's slowly more solutions to that as well. Combine that with stuff like socket.io and the emerging WebGL, and you've achieved parity with most Flash and Unity games.
That said, there are drawbacks to Javascript. Namely, it is much harder to protect the code from being stolen or hacked, and depending on various factors, you're cutting out a subset of users who might be running IE8 and below. There are solutions to these problems, and there is one major drawback of Flash (doesn't work on iOS), but generally, these should be pointed out.