EDIT: In the original question I talked about spans in headers, but because of misguided answers I edited the question to better reflect the fact that the keyword is catchphrase not span. Thus the following reference is perhaps a bit obsolete, but I'll leave it here anyhow.
N.B. Also though I talk of font size here the question is not about font size either. I'm aware of this: Is heading (h1, h2, h3...) font size relevant for SEO? and according to that font size does not matter. I've only mentioned font size to make it clear that the catchphrase is of lesser importance than the main header and that it is quite long, which would be impossible if it was displayed with your standard gigantic h1 letters.
I noticed there is quite similar question, which says it's ok to have spans in headers: SEO of <span> in <h1> header
If someone more knowledgeable regarding SEO could tell me which of these is better in SEO point of view or is there any difference:
I presume Google will at some point penalise adding too much stuff in to the header?
My cool header - A longer catchphrase complementing the header that with added markup is likely displayed with smaller font size
vs something like this:
<h1>My cool header</h1>
- A longer catchphrase complementing the header that with CSS styling is likely displayed with smaller font size