The force of the "then" in Matthew's account is "at that time," rather than "afterwards"; therefore, Matthew is locating the beginning of persecution at the time of the things that had been mentioned before. Mark seems to be addressing the persecution as if it was occurring within the stream of events mentioned previously (false Christs, wars, earthquakes, famines, etc). Luke places the persecution as occuring before (at least) the terrors and the signs in the heavens (v. 11). So, there isn't really any difference, after all.
We are told that believers will be handed over (betrayed would be the implication from Mark 13:12 and Luke 21:16) to be afflicted (persecuted, as in NIV, is not as precise), and killed. Luke specifically (v.12) places this as occurring very early in the scheme of things, and in doing so, certainly emphasizes early Jewish opposition to Christianity (note: synagogues). However, that cannot be the exclusive scope of the persecution since kings and governors (plural) are also mentioned in the same phrase. Mark and Matthew are less specific, implying that persecution will be the case near the end or even throughout the period in question.
We are also told that believers will be hated (Matthew 24:9). The word refers to moral choice, i.e., picking one above others, and is the same word used to convey the same thought in Luke 14:26. The notion is that the world will like everything better that it likes Christians. This will be the case globally, in all nations. It serves as an interesting counterpoint to the gospel being preached in all nations (v 14).
Packed into the reference to “all nations” is a broad sense of elapsing time; for how long does it take to be hated in each and every one of the cultural/linguistic groups (Koine: "panton ton ethnon")? One has to become known to each and every one in order to be detested in each and every one. Therefore, to see this discourse merely in terms of Rome in the first century is a mistake. When this was written, there were boundaries and there were barbarians--it was known and understood that Rome did not include all of them.
At that time (tote, again) many will fall (into a snare), which implies not so much apostasy as it does deceit, which is reinforced by the mention of false prophets. Associated with this fall is their betrayal (handing over) and detesting of one another. So, false prophets will arise and cause many believers to stray resulting in internecine detestation and betrayal. Anything in any age which foments hatred toward brothers or sisters in Christ is false absolutely, it's source will always prove to be devilish rather than from God. Listening to it will turn the persecuted into persecutors!
Through the multiplication of lawlessness or a lack of restraint (wickedness is not a good translation), love will be made cold. The voice of the verb is passive, and so refers to action that is being done unto the subject or is arising from the action of another. Therefore, the chilling believers referenced are not volitionally active, their love does not grow cold by choice, but chills as an effect of being exposed to the multiplication of lawlessness. The wear and tear of exposure to lawlessness is insidious and lethal.
What is shocking to me in all this is the use of the word “many” (Koine: polus). It refers to a whole bunch, to a great number. Jesus was saying that things will progress at the time in question in such a lawless fashion that the occurrence itself chills the love (agape) of many or most! It is possible, maybe even probable, for believers to fall into despair and lose hope in the face of lawlessness and to end up hating the lawless. What happens to the Great Commission, and Christlikeness, in such a circumstance?
Given such a description, one has to wonder if Jesus will find faith when he returns? Life lived in this age leading up to the coming of Christ will be an assault on our faith. There is a challenge to meet, there is an occasion to rise to, there is something to be proven, and it won't be done for us. But the one who bears under the assault to the end will be saved!
According to the Olivet Discourse, then, persecution of those bearing the name of Christ will start in the midst of the signs stated in the first third of the address and will proceed until the end of the age. We know the entire span of the age is envisioned because disciples cannot be hated by all nations until all nations have been confronted by the gospel, and because we are told that those who endure to the end will be saved. Being hated is something all true Christians ought to anticipate throughout all time and everywhere, but when it comes our way, we can't let it turn us into a hater in response.