For web browser game, flash or unity, which is better?

AFAIK, unity has its own development tool, free and easy to use, but flash is more common in browser

Also, unity engine is written in C++ while flash use actionscript, so, performance-wise, is unity faster?

Regards

Better is subjective.

It depends entirely on your game and your proposed user experience.

If you want a 3D game experience that Unity provides you may have a difficult time simulating that with Flash.

If flash is adequate for your game, Unity would be overkill.

Use the tool that you are most familiar with.

It all depends on what kind of game do you plan to develop.

Facebook social games for example, are often made with HTML5 and/or Flash, but in my opinion, Flash's renderer is really too weak when compared to Unity's (keep in mind that Unity can be used to create 2D games with the right setup.)
A 3D or 2.5D game should preferably be created with Unity as you have all (?) the tools you might need to carry on with the projects and evade tough and complex stages that the Unity team has already done for you.

Afterall, think about what do you exactly expect from the "engine" you want to work with. But at the end of the day, learning C#/C++ Game Programming is far better than investing time in Flash if not needed.

It's important that you think about the monetization side of things. There are far more flash game sites than unity or HTML 5 game sites. So unless you are funded upfront to make a HTML 5 or Unity based game, you might be limiting yourself a bit in terms of monetization.

If you are doing 3d, you can do it in either flash or Unity, although I'd say that Unity is probably the better choice. So to some degree, what type of game you are making is important in deciding.

If your game is going to be 2D, I would recommend flash. It is much more widespread and likely an easier environment to work in. If it is going to be 3D, go with Unity.

I agree...trying to 2D in Unity is tough, but a lot cheaper (read: "free") than Flash. I ended up having to write a plugin so I could do 2D in Unity the way I've always done it in Flash: https://www.assetstore.unity3d.com/#/content/10160