What you can gain by filing your company in Estonia is less bureaucracy. The talk is that Estonia is a lot in e-government, so I suppose that means you can do a lot of filing stuff very conveniently on the Internet. Or if you employ people in Estonia, the employment laws may be less strict than in a country like Germany.
If you plan to operate out of Germany, I don't think you'll gain much by registering a company in Estonia. If you want to move to and operate in Estonia, it may be well worth a consideration.
As mentioned, in the past people filed companies in the UK to avoid the 25000 Euro investment required for a GmbH. But that's gone with the UG.
However, the company itself very likely has to pay German company taxes and need German business permits if you operate from Germany / generate the income in Germany.
But if you have 10 Estonian developers in your Estonian company doing programming for you in Estonia and you are only the founder/investor living in Germany, you probably wouldn't have to pay anything in Germany if you don't pay out profits.
To get a dependable answer you really have to discuss that with a tax lawyer. And finding one which can deal with multinational businesses is going to be really tough and presumably expensive. Which is another reason why this whole thing is more headache than gain, IMO.