Here's my response in the other thread:
Yes, it would be very likely that a different sperm would give me only minor physical differences, but retain the same mental capabilities. However, another sperm could carry vastly different genetic information which would in turn no longer be recognizable as what I consider "me".

Had another sperm penetrated the egg first, there may not even have been a birth. Could I have been anyone other than me? Physically, yes. Mentally, no. How much did my upbringing effect who I am? If I had a different genetic makeup, I could have had a completely different hardwiring that would change completely who I am. I would no longer be me. "I" wouldn't exist, and a stranger would be responding.

What is the probability that a percentage of the sperm would still lead to "me"? According to http://humrep.oxfordjournals.org/cgi/content/full/14/8/2036 the variance in sperm is quite high. So, as far as who "I" am, I consider myself extremely lucky to have come to be.