One is not better than the other, but they are different machines.
1. Circular Saw
A circular saw is great for rip cutting. Rip cutting is when you have to make a long continuous cut going with the grain. It can also be used for cross cutting (against the grain and typically a shorter cut). Although it can be used to cut smaller boards, it is often used for plywood. In order to keep a circular saw straight over a long distance it would need a track. You can also clamp down a straight edge of some sort and run it along that line.
Circular saws come in varying sizes (it’s the blade that is measured) but an average is 7 ¼ inches. They also come in right or left handed so if you’re a leftie pay extra attention or else you’ll have the same issue you have with scissors just with a more powerful set of scissors.
2. Miter Saw
A miter saw makes really accurate cross cuts. As I just mentioned a cross cut is against the grain and parallel to the longest edge of the board.
Keep in mind sometimes a miter saw is called a chop saw, although a chop saw is actually for metal but the design of the machine is very similar, a chop saw is just made of different material so that it does not catch on fire while cutting metal and sparks are flying. But back to our miter saw. These come in sizes as small as 7 inches and all the way up to 12”. You might ask, where is that size measured from? It’s measured by the blade across the center.
Newer Miter saws often have a laser so that you can more easily see where you’re about to cut.
Which one is more expensive?
A circular saw is going to be a lot less in cost than the miter saw. Circular saws can range from $40 to a small one to $100 for a little nicer one.
Miter saws can range from $200 to $600 at most big box stores. You could find either of these in gently used condition at estate sales, craigslist, or on ebay.