First off, Java is a programming language that can make dynamic programs available through just your web browser. So understand that with Java-based trading, your forex trading platform will load within your internet browser (such as Internet Explorer or Firefox).
One of the potential upsides of a Java-based trading environment is that because there is no need to install any software, you can use nearly any computer to access your forex trading account. With a downloadable trading platform, you will usually be tied to a single computer for your trading because any other computer that you would use would need to have this software installed as well.
A potential downside of a Java-based forex platform is that downloadable platforms tend to have many more features, such as a newsfeed, advanced charting, and possibly even trading signals. A Java-based platform will likely have not much more than you need in order to place trades, and you will need to use some external charting program in order to view price data.
FX trading platforms that you have to download and install onto your computer tend to be highly refined to the point that they will very rarely, if ever, crash. Brokers know that they could lose many customers if they use a software which is prone to crashing, so they will put significant resources into making sure that their software will be stable.
Your internet browser is much more prone to crashing than is your trading software (usually), especially if you are surfing other web pages or checking your email at the same time. If your browser does happen to crash or shut down, and you have trades open, it is hard to predict what will happen.
Either way, it is always a good idea to keep the phone number of your broker on hand just in case you should have trouble with your trading platform. If for some reason your Java-based trading environment were to crash while you had trades open and you were unable to bring that data back up on your screen, it would be wise to call your broker and close all open positions.
Ideally, you would want to choose a forex broker that offered both a Java-based trading environment as well as downloadable software. That way, you could enjoy the stability and features of the downloadable software, but also be able to log into your trading account from a computer that does not have the software installed.