How do the eschatological doctrines of Charismatic or Pentecostal groups that hold to dominion theology differ from other Charismatic or Pentecostal groups (e.g. Assemblies of God) that do not?
Overall, there is no absolute consensus in eschatological views among Charismatic adherents to dominion theology. If a particular group decides to teach eschatology at all, they often teach all the main threads of doctrine and let people learn on their own. Dominion theology, in effect, could fit in most of the popular eschatological timelines.
To use the Assemblies of God's doctrine as a starting point, though, I will compare with some popular eschatologies in the dominionist camp.
Looking at the AG's site, it is evident that they believe in a pre-tribulation rapture. This is a doctrinal point very often argued against by adherents of dominion theology, because of its tendency to create a defeatist attitude among believers. In the dominionist's view, the Kingdom is always advancing towards its ultimate fulfillment, and there is no need for God to remove us from the earth during the Tribulation. God will be doing great works of which we will be a part, and the Church will never give up on influencing the world. For some dominionists, this would mean a post-tribulation premillenial rapture (see IHOPKC's Omega Course).
Other popular eschatologies that fit very well with dominionism are postmillenialism and amillenialism (postmillenialism being a literal interpretation of the millenium, and amillenialism being a symbolic unknown time period). In both, the Church is advancing the Kingdom of God and preparing the earth for the second coming of Christ. The "tribulation" here is figuratively interpreted as God's judgements along the way, of which we participate, as the Church takes complete dominion of the earth for God.
See the book Victorious Eschatology for a little more on some of these views.
This is a very subjective question, but the best answer is that it completely depends and differs from church to church, church leader to church leader. Some churches adhere to doctrine such as Romans 13:1-6, which teaches we should not question our government and authorities since they are ordained b God, and yet some adhere to a more interpretative view that they can do whatever they want including against their own government, despite Romans 13. Some may claim that dominion theology is anti-faith and anti-bible, but there are justifications for about everything in the bible if you torture it enough. Things have changed over the decades as dominion theology often involves pushing a particular political candidate or position, which ironically is one of the only ways a church can lose its tax exempt 501(3c) status, and hence other churches say out of politics for this very reason.
In her 1989 book Spiritual Warfare , sociologist Sara Diamond discussed how dominionism as an ideological tendency in the Christian Right had been significantly influenced by Christian Reconstructionism.
Diamond claims that Christians are Biblically mandated to 'occupy' all secular institutions has become the central unifying ideology for the Christian Right."