The German word Zungenbrecher translated literally means tongue-breaker. Is this an indication that tongue-twisters in German are worse than they are in English?

I'll let you evaluate that for yourself! But more seriously, tongue-twisters are a great way to practise pronunciation, particularly with sounds that are similar, or words that differ only by a letter or two. I have German tongue-twister collections for vowels and consonants.

More fun though are the tongue-twisters where a word is repeated, often with double meanings. These are called battologisms. A particularly German genre of tongue-twisters or rhymes is the Schüttelreim (shaken rhyme). These consist of pairs of lines in which the initial consonants of the last two stressed syllables in the lines are swapped, creating new words. There's some similarity with Spoonerisms here. Just don't get your tongue in too much of a knot!