Think of Cromwell as an “accidental democrat”. He believed in power and position based on ability, and that everyone, regardless of class or religion* should have the opportunity to reach that position. Everyone was equal in the eyes of God, and everyone was equal in the eyes of the State and subject to the rules thereof - be they King or Carpenter.
It was this that put him into conflict with the King and, later, with Parliament.
Partially, but he also brought it on himself.
You can probably argue that by the time of his execution Charles completely embodied the idea of absolute monarchy, and that, ultimately, this contributed greatly to his trial and death, since he represented everything that was politically anathaema to the new State.
What’s important to remember however is that Charles embodied this not just because he was King, but because he himself cultivated this image.
Why? Well Charles was a fervent and unwavering believer in the Divine Right of Kings. This was the idea that the King was accountable to no-one but God and that, by definition, not only was the King not subject to the will of his people and the state but that to ever go against the King’s wishes was to go against the Will of God.
Now ever since the Magna Carta, most English Monarchs had been smart enough not to mention the whole “Divine Right” thing in polite conversation (at least not unless they had a sufficiently large army to back them up). In return, the ruling classes (be they Barons or Parliament) had agreed not to bring up the matter and question its validity in an age no longer plagued by rampaging Vikings or anti-Norman sentiment.
So basically, by the 17th Century the unwritten rules of government where that the King could do whatever he liked as long as:
- He asked Parliament first and at least pretended to listen to what they were saying.
- He didn’t mention the whole “Divine Right” thing within their earshot or brag about it to his mates.
- He didn’t do anything outrageously and obviously fucking stupid and/or expensive.
So when, after a few years in power, Charles starts saying that:
- I don’t need your permission to do anything. I’ll ask you sometimes if i think you’ll agree with me and even then only if i remember.
- I’ll tell the whole fucking country if i want.
- If i want to start expensive wars with Spain and France i will. Oh yeah, and i’m putting my mate Buckingham in charge of the campaigns, even if he is one of the worst Generals ever.
You can imagine that politically he wasn’t exactly making friends or adhering to the principles of English Government. The lines for the Civil War were drawn.
So you can probably imagine that, since Charles had come to represent everything that the war had been fought against it would be impossible not to do something suitably extreme with him after the war.
Don’t make the mistake though of assuming that the moment hostility ceased, Charles was doomed to the executioners axe. Truth be told, no one knew what to do with him (mainly because they hadn’t expected to win). The concept of Divine Right may have run contrary to their political beliefs, but the step from that to killing a reigning monarch was enormous. Sure, they’d mouthed off about it, but no one was seriously expecting to have to go through with it - it was a Magna Carta situation again - beat the King, humble him a bit, then go back to business as usual.
This is where, again, Charles’ own behavior and beliefs came into play and helped seal his fate. Not only would he still not shut up about the whole issue (talk about a sore loser) but he also knew that Parliament was unsure what to do with him and played an incredibly complex political game with himself at the centre and the Army, Parliament and the Scots/Royalists as the rival players.
This was a massive risk to take - Charles was now deliberately gambling with his own life. He knew that the longer he could stall a decision on his fate through political manoeuvring and playing the unrepentent Absolule Monarch, the more likely Parliament was to chicken out of making any decision at all and collapsing in on itself.
It was an all-or-nothing play of course, because now not only did he continue to embody everthing that the war had been fought over, but he also posed a significant threat to the stability and indeed very existence of the new State.
“I am King and therefore i am the originator of law, not subject to it. Kill me or agree with me. I ain’t moving” was pretty much his message.
He was trying to call Parliament’s bluff.
He would almost certainly have got away with it too, if Cromwell hadn’t stepped in. Cromwell, backed up by the army, forced Parliament to put its money where its mouth was. It was he who almost singlehandedly forced through Charles’ conviction for treason, it was he who literally forced the judges to sign the King’s death warrant and it was he who pretty much made sure that events progressed to their gruesome end.
I’m guessing neither the King or Cromwell was someone you’d ever want to play poker against.
So i guess the short answer to your question is this:
Charles I was defeated for what he represented, but he was killed for who he was.
*unless you were a catholic obviously 
