Both indicate a change, but it's really the difference between present simple (general fact, regular habit) and present continuous (a progressive activity at this moment).

To compare the two sentences, they need to be in the same verb form. For example, if this is a change in a person's behaviour which is happening at the moment, you could say either 'She's becoming selfish' or 'She's getting selfish'. In this case, 'becoming' and 'getting' have exactly the same meaning. 'Getting' is simply more informal. You'd use 'getting' in casual speech or informal writing, and 'becoming' in neutral or formal writing and more formal spoken settings. Note that you can generally replace 'become' with 'get', but not vice-versa.

is getting selfish: implies something that is currently happening. becomes selfish: implies something that may happen at a certain time of point or happens often. It is more in an abstract context where "getting selfish" is more direct.