For some, the usage will not in any case be a matter of choice. Within Biblical Studies, the usage is now so widespread that some authors will have had it imposed on them by publishers who make this an element in their house style. Indeed, the usage is much more widespread in our area than it is in any other discipline, and by a country mile. Bob speaks of "the increasingly accepted international scientific standard of BCE (“Before Common Era”) and CE (“Common Era”)": but I am not sure that it is so widespread. I rarely hear it outside of our field.
Bob's focus is on the BC / AD labels as they are used by Christians (note the title), but the difficulty is that everyone uses these labels. As Chris Heard points out in comments, Richard Dawkins uses it without apology.
Moreover, I don't think the term "dating system" is quite right. The dating system is the same, on BCE / CE and BC / AD; it is the labelling within the system that differs.
I would like to comment also on the following:
While the Gregorian calendar accurately represents years of 365.25 days, Dionysius’ calculations skipped the year zero, jumping immediately from the year 1 BC to the year 1 AD. The result is a calendar that claims to be based upon the birth of Jesus, but which skips the first year of his life.
There is also no "year zero" on the Gregorian calendar, so bringing it up in this context is a bit of a red herring. Dionysius did not "skip the year zero"; he did not factor in a year zero. It is true that there are astronomical calendars that subsequently have factored in a year zero, but this is not relevant to the Gregorian calendar, or to Dionysius Exiguus, which work with a transition from 1 BCE to 1 CE. There is no question of the first year of Jesus' life being "skipped".
Bob goes on to note that Jesus' birth can be located around 4BCE because it happens near to the death of Herod in Matthew 2:
If we add to these 4 years the fact that Herod the Great did not die immediately after the birth of Jesus, but, according to Matthew, ordered the death of all children two years of age and younger in an attempt to kill Jesus, we can add an additional two years to the birth of Jesus, making his birth approximately 6 BCE. If we also add the missing year zero, it is most likely that, according to the Gospel of Matthew, Jesus was born around 7 BCE!I doubt that we can be too precise about Matthew's dating. I am a bit of a sceptic when it comes to the historicity of Matthew 1-2. At best, I think he had a vague idea of the rough time when Jesus was born. The murder of children of two years old and younger may also say nothing about the time elapsing; it may have to do rather with Herod's attempts, as Matthew conceptualized it, to be thorough. The extra year for year zero is not necessary and should be dropped too.
Bob goes on:
Thus, the BC/AD system is fundamentally flawed in that it misrepresents the birth of Jesus by approximately 7 years. This means that Jesus’ ministry did not begin around the year 30, but instead around the year 23. Likewise, Pentecost and the origin of the Christian Church should not be dated to “33 AD,” but to about 26 CE.
The "year 30" is presumably based on Luke's notice that Jesus was "about thirty years old" at the beginning of his ministry (Luke 3:23), working forward from 7 BCE to 23 CE. But there are other indicators of date here in Luke, most specifically the fifteenth year of the reign of Tiberias (Luke 3:1), which places the beginning of Jesus' ministry in 29CE. Bob's "year 23" can't be right. Moreover, 23 CE is too early for the note that Pontius Pilate was governor of Judaea (Luke 3:1), which makes 26 CE the earliest possible date for this (26-36 CE).
I have one more concern. Bob notes rightly that Matthew dates Jesus' birth near to the death of Herod the Great (Matt. 2.15, 19-21) and that Luke apparently dates it at the time of the census that took place "when Quirinius was governor of Syria" (Luke 2.2). Since the latter probably occurred in 6 CE, Bob suggests that there is a 10 year (or so) discrepancy between the dates of Jesus' birth in Matthew and Luke. However, this cannot be the case. Luke 1.5 follows Matthew in dating the action during Herod's reign. Unless he thought that Elizabeth had a ten-year pregnancy, Luke is not dating Jesus' birth in 6 CE. What on earth he is doing with the mention of Quirinius in Luke 2.2. is a mystery, but my guess is that his dating is a bit off. He has things roughly in the right decade or so, but he is not precise enough here for us to work out exactly when he thought Jesus was born. (He is a bit more confident when he gets to the beginning of John's ministry, on the other hand, in 3.1).