I truly believe there is much more that goes into a compatible relationship between two people besides this theory.
For myself, personally, I have dated guys that was JUST like me personality wise (introverted, homebody, not overly emotional, more on the "serious" side, conservative, reserved..)
I have also dated opposite of my personality, (extroverted, partying type, loud, more emotional than I was, goofy, outgoing) and honestly, both guys I dated had pros and cons... one personality did not fit better than me more than the other.
The guy that was opposite of me had his pros, but he also drained me, he was more sensitive emotionally than I was and to HIM, I constantly made him feel like I was not into him when I was - I'm just not overtly PDA with people. He loved going out all the time to the bars and party and drink, I hated it, so that caused friction...
On the other hand, the guy I dated that was pretty much MYSELF but a guy also had an equal amount of pros, but because we were so similar in terms of personality, we did at times "get" each-other BUT at the same token, it became sort of boring between the both of us...
I think it can go either way, the "opposites" attract or the "same" attraction I believe doesn't really count.