Scriptural prophets generally go out and preach to groups of people who don’t believe in their teachings or may outright hate the prophet or group of believers. They put their lives in danger and face criticism to their arguments.
Modern prophets tend to only preach to believers. They travel around the world to wards and stakes that welcome them with open arms. They tend not to have to face criticism—lawyers, the PR department, and unofficial apologists tend to deal with most of the criticism.
Scriptural prophets generally gave up all their worldly wealth to preach the gospel. They often come from humble circumstances, but if they didn’t they may have given up their wealth when they go to preach.
Modern prophets get paid a stipend of at least 120,000 USD a year (along with other substantial financial benefits). Most modern day prophets come from wealthy families, and most modern day prophets themselves are fairly well-to-do. None of them sacrifice financial wealth in order to preach the Gospel.
Scriptural prophets sometimes prophesy of future events. When they speak directly with God they tell the public that God spoke directly with them and that they are delivering God’s message to them.
Modern prophets don’t seem to ever prophesy of future events. They sometimes hint that they speak with God but it is difficult to say for sure. Virtually any stories of them seeing God come from third party accounts. One is never certain if the message they are delivering came from God or is their own opinion based on their reading of scripture.
Modified from here