I think you are mixing a few things up because of a slight misinterpretation of the cartoon you posted after this.
Really random passwords (using letters, numbers, and special characters) are always safer than a string of only letters or numbers of the same length. It is just simple math.
Say you got a 10 char password. An alphabet only password would have 26^10 = 1.4^14 possibilities. If you include Capitals, it would be (26*2)^10 = 1.4^17 possibilities.
A 10 char password of only numbers would only be 10^10 = 1.0^11 possibilities.
Now, if you take all characters, you would get (26+26+10+20)^10 = 1.4 ^19 (I took 20 for special characters, not sure about the exact number
In the example of the words as a passphrase, what you actually do is, you change the "dictionary" to include more than just the 26 characters of the alphabet, and instead you include say 20,000 words. You actual password would in this case have 20,000^4 possible outcomes, or 1.6^17 possibilities.
You can see already, that if you use the same amount of random characters as the length of the total characters in the words, your number of possibilities would be way way higher than this already. (correct horse battery staple is 28 characters including spaces, in a random password this would mean around (26+26+10+20)^24 = 8.5^45 possibilities, which is much much much more than the previously mentioned 1.6^17 for the words.
I'm sorry if the above is a bit difficult to read, but I hope my point is clear.
A final very important note: humans are not capable of creating random passwords . Even if you think you do random picks for letters and numbers, humans tend to pick certain letters and numbers or combinations of them more often than others. Do yourself a favor and use a random generator and a password manager to avoid having to remember this.