Celebrim
Legend
I start with neither. I usually don't have my PCs internal life worked out until play is well underway and I rarely think of mechanics first. I guess I start with an elevator pitch to myself, usually in the form of a one-liner. Which is to say I begin with an amusing concept for a fictional character that I try to work up some enthusiasm for.
For example, my current Fate Core PC started with the phrase: "He's the Sorcerer Supreme of Bensonhurst (Brooklyn)".
Followed by: "He's half Jewish, half robot (on his father's side)". It's a sci-fi campaign.
This works particularly well in Fate, where amusing phrases are part of the PCs stats.
Thus was born Abraham Disraeli Gears, rabbi of Temple Beth Moreau.
I use a similar approach even in crunchier, gamier systems. My favorite Mutants and Masterminds PC began with, "He's the Egyptian God of Mexican Wrestling!" -- (I was watching a certain episode of Angel at the time...).
I'm not even sure what to make of that. Which is a good thing.

So, I definitely recognize FATE as an attempt to solve this problem and make WYA crunchy. In practice, most examples I've seen of fate involve WYCD tags, even in the FATE rulebook. So, again, how this plays depends heavily I think on how the table thinks about the system.
It sounds to me like you are going into play in FATE with neither WYA or WYCD actually decided on, with the expectation that you'll answer both in play. Does that sound right?
Instead you seem to go in armed with broad sterotypes, (jewish, robot, sorcerer), that just about anyone could mine (jewish for example contains a lot of depth as a sterotype and could go several ways), but ones you've wildly subverted in an over the top zany manner. The subversion of a stereotype is something I definitely approve of, but I don't think I can teach how you get to a Rabbi with a robot father (how does that even work, on several levels? Did you have that worked out before play?). You don't seem to have a methodology for generating that initial concept, and if you do I want to hear it.
Do you always play zany characters?
Your M&M character began with a WYA concept. In fact, I'm pretty sure both described characters did, because I have only a vague idea what the characters are capable of and if WYCD had been prioritized I think you could have described them in WYCD terms in just as much language ('brick', 'paragon', etc.). I know 'sorcerer' is really broad WYCD (when does that tag not apply to solving a problem?) . Did you narrow it. Or more generally, starting with the broad pitch, where did you go from there?
How exactly did you 'tag' you FATE character? Were 'Sorcerer Supreme of Bensonhurst' and 'Half Jewish, half robot (on his father's side)' actual aspects you invoked?