Because they are played directly from the server where they reside they will usually be susceptible to internet traffic. This means if many people are on that server at one time the games will run very slow and the experience will not be fun, also flash games have less encryption on them. Also while you are playing it is constantly uploading and downloading info to your computer so you are using greater bandwidth while playing then a download game would. This is also true if you are trying to download other things from the internet at the same time you are playing the game. If you are playing a multiplayer flash casinos game you will find that there is sometimes lots of lag time and that is annoying for you and the other players you are playing with. No one realizes you are lagging and get frustrated because you are always holding up the game.
Download casino games are preferable for several reasons. They offer better protection for the player by using a more secure connection type with the server the casino is located on. Because they are running directly from your pc they will run faster and smoother. Also there is usually a better choice of games in a download casino then in a flash casino, plus with a download casino you can quickly switch from game to game. In a flash casino you would need to stop your connection and click to open another game.
When push comes to shove it all comes down to personal preference. Personally I feel safer using downloaded casino games, but I know many people that want to play roulette or blackjack from work and do not want to have the casino software on the company computer or they are unable to download the casino software due to company security policy so they like the Flash Casinos.
One thing I have learned is that if you want to play the multi player games like poker in the Poker Rooms you have to use the flash casinos this is because you all have to log into the same server so you can all play together and to do it from a downloadable game you would all have to play from one of the players computers.
I recommend you try both these types of games and see for yourself which game type is better for you or if you even see a difference at all. Then you can make a more informed decision on which type of casino game you wish to continue to play.