I'm not a native English speaker.
for me, those two sentences are the same meaning:
one): it was more about me being obsessed with the job.
two): it was more about that I was obsessed with the job.
In both your sentences the subordinate clause headed by BE is the object (or 'oblique') of the preposition about.
Terminology varies widely, but I'm only familiar with 'object complement' as a designation for a 'predicate' or 'predicative' complement of a verb which characterizes the verb's direct object:
The dean named Prof. Sartorius chair of the committee.
We painted the room red.
Please put it on the shelf.
Your number 'two' is at best only marginally grammatical in contemporary English. There are only a few prepositions which license full finite clauses ('content' clauses) introduced by that as their objects; Huddleston and Pullum, The Cambridge Grammar of the English Language, 2002, p.971 lists these:
but considering except given granted
in notwithstanding now provided providing
save seeing so supposing
That cannot be omitted with in or with but in the sense 'except', and with so the use with that may have a different meaning than the use without it. That can be omitted with the others (but the omission with notwithstanding and save has a very old-fashioned ring).
These prepositions may take content clauses as their objects, but that must be omitted:
after although as as if as long as as soon as
because before for for all if in case
lest like once since though till/until
unless when where whereas
CGEL also lists (p.623) a handful of 'prepositional expressions' which may be followed by that clauses: the that may be omitted with
in the event,
on the grounds,
for fear, and
on condition but must be included with
With any other preposition I'd advise you to stick to the gerund (-ing form) clause used in your number 'one'.