Amish are much much stricter about the use of technology, how much they are willing to buy at the store, clothing options. Mennonites are more apt to have a shared black or blue car that is used to take the whole family and the neighbors to church, and church is a separate formal building. Mennonites also usually have electricity and there's at least one phone line for the neighborhood, if not for the household. Amish often don't have a separate church building, they just use whatever structure is handy--sometimes a barn. Church services are different too, Mennonite services are more often at least partially in English whereas Amish services are always in German.
The Amish have strict rules for dress and how hair is supposed to be cut/shaved for men, styled and covered for women, certain types of bonnets for single vs. married ladies. Mennonite women usually just do their hair in a bun and wear a little white cap over it, wear short sleeved dresses of storebought fabric that may be calico prints if they want, with a different style collar according to preference. Their dresses tend to be a little more tailored. Mennonite men dress in a style that isn't very far off from "English" business-casual, with a hat, and can shave if they like. Amish women wear only solid-color dresses that must have a sort of black or navy blue over-dress/apron, and a specific style of bonnet that covers the whole head. Amish men wear black or navy blue pants, hat, and have to do their beards a certain way.
Also, should your immediate family leave the community, your Mennonite cousins will still be happy to see you and hang out with you, while your Amish cousins will continue to shun you.