The Hanse is in my opinion the most powerful UB in the game. You can get up to 12 trade routes I believe (assuming Petra and the Colossus). If that's correct, you can get up to a 60% production bonus IN ALL CITIES once you have those trade routes going. This is a bonus no other civ can replicate; Germany is capable of almost twice the production of other civs.
It also has great synergy with the Freedom policy that makes you gain influence with CSs you have a trade route with.
Lets start with you get 8 Trade Routes, 10 with wonders. Reaching that value is completely unrealistic, At most you will usually see about 6 before the game ends or is a few turns from ending. When you get Hanse, unless you hunt down the top line, you will likely be at 4, maybe 5. You will probably remain at that value for a good while after getting Hanse too, unless you rush Biology...
As for the effect, it is completely relative to how much hammers the city is producing. An average sized 10 hammer city gaining a 20-40% bonus would only leave it at 12-14 hammers, a nice boost but nothing insane. A small developing city with for example 4 hammers would barely notice an improvement. So the only time you actually feel the power of the Hanse is during the late game. When your cities have 20-40 or more hammers. When you have plenty of Trade Routes.
Don't get me wrong, I think the Hanse is great and gave Germany the boost they needed. However, due to the fact it is only really effective during the late game, in my mind at least, brings it down a few notches.