As mentioned above, Appodeal is a “mediation” plugin. That means when you request an ad, it goes through multiple channels (demand providers) until it finds an ad. This should, 99.9% of the time, guarantee that you get an ad. Many individual ad provider have low “fill rates” which means you might not get an ad at all. Many developers end up building their own mediation by including multiple plugins. You call ad provider A to load an ad. If you get an error, you try to load an ad from provider B and so on. Appodeal does this for you in a more efficient way. AdMob is one of the networks providing ads to Appodeal and then to you.
To make your own mediation work, you have to include all of the SDKs in for every ad network you are using. Since Appodeal uses many different networks, the Appodeal plugin has all their SDKs included making the Appodeal plugin rather large. AdMob by itself, since it only provides one provider’s worth of ads, is relatively small. If you were to do your own multiple ad provider setup, you would find all your plugins added up together would start approaching the size of the Appodeal plugin.
Finally as mentioned above, Appodeal needs a high number of daily impressions, on the order of 10K per ad type, to get the efficiency that mediation brings. At that level you get the ad networks competing for your impressions which drives up the value.
With Admob, you will only get AdMob ads with it. If your app isn’t generating high numbers of impressions, it could be a better performing solution for you.
The Appodeal plugin, while free, is considerably larger. Some developers want to keep their app sizes down (in particular on Android). It adds about 14mb to your project.
There are likely other differences as well but to me those are the main ones.
Rob