I used to use a hand held mixer, because that is what my mom used. Although it does the job and mixes batter for baking, I think its performance in the kitchen is pale in comparison to a stand mixer.
One of the biggest advantages I noticed when I purchased a stand mixer, is its power. A stand mixer can mix thick batter easier than a hand held mixer can.
I also like the freedom a stand mixer offers. I can leave the mixer running while I get other ingredients I need for a recipe. Conversely, a hand mixer requires me to stand next to the bowl and hold the mixer. This makes me feel tied down in the kitchen.
Another advantage of a stand mixer is it comes with multiple attachments. A hand help mixer only comes with beaters. Conversely, a stand mixer comes with multiple attachments. These extra accessories allow me to knead bread, whip meringue, mix cookie batter and more. I also notice the difference when I make cream cheese frosting. It turns out fluffier when I make it with my stand mixer. I think this is a result of the speed at which it is capable of mixing. All I know is it turns out so much better with my stand mixer.
One advantage a hand mixer has over a stand mixer is that it is easier to clean. All I do is pop out the beaters and clean them. Then I wipe down the hand mixer body. It is ready to be stored until my next use. With a stand mixer, I have to take out the beater, detach the mixing bowl from the base, and wipe down the entire machine. Once all the parts are clean, I have to assemble them back together again.
Since both the stand and the hand held mixer are useful in the kitchen, I like to have both available in my kitchen. Sometimes when I just want to mix up some eggs, it is more convenient to use my hand held mixer. When it comes to more complicated thicker recipes, I prefer my stand mixer. You may find you like to use both styles of mixers in your kitchen too.