Charismatic Christianity is a fact of Christianity today (probably globally the majority?), as is non-charismatic Christianity.
The distinctives of charismatic Christianity are an emphasis on experience and exercising the full range of spiritual gifts today. These aren't necessarily exclusive to charismatics, for example many non-charismatics sharing the puritan emphasis on affections, but you won't find charismatics who lack these two emphases. That's not to say those things define them - just look at the endorsements on Pierced for our Transgressions to see that it's the cross that we hold in common. Cross-centredness is an evangelical distinctive, not a distinctive when we contrast the charismatic and the non-charismatic believer.
Bonnington argues that to some extent the shape of our Christianity depends on our integrating points. I've heard people suggest that personality plays a big part (y'know introverted non-charismatics, extroverted charismatics - if so I'm something of an exception as an introverted charismatic, along with a lot of others I can think of!) but it's the Bible that drives all good-hearted believers. We all want to be 66-book Christians but we inevitably have favourite points which end up carrying more weight for us.
So take cover and view some stereotypes!
The non-charismatic might turn most to Romans to draw their Christianity together - this is to stereotype a propositional and doctrinal focus. Doctrine and propositions are things to die for.
But, three types of charismatics might take a different emphasis. Some turn to 1 Cor 12-14 and major on the importance of gifts in the body of the local church. Some turn to Luke-Acts expecting signs and wonders and power for mission with a high value on baptism in the Spirit. Some turn to Matthew-Mark-Luke and look for Jesus-style kingdom ministry with much healing, intimacy and the like.
I'd argue all four belong in evangelicalism but when they try to live together things can be a bit tense, because discipleship, ministry, evangelism might begin to look really different depending where you're coming from. Somehow we need to work it out. We can't just say, do it on my terms (and leave your distinctives at the door) so we need a way to live together, celebrating one another's approaches and learning from them. Taking the best from each other, recognising that we have differences, not sweeping them away or saying they don't matter - developing robust enough fellowship that we can actually disagree and still love one another and work with one another. Understanding those who emphasise some things differently and realising that we can learn from them and work with them is a beginning.