MMM aims to report the true incrementality of your media spend. Google Analytics reports the attribution of each media - it doesn't tell you how much of that was truly incremental. Therefore, it is expected to have major differences between MMM and Google Analytics reported attribution.

Example: Your Google Search Brand looks to be much more efficient according to Google Analytics - however, not all of your brand searches are truly incremental and driven by media. Many customers knows you already and come to your websites, regardless if they have seen your ad or not.