We use, almost exclusively, electric flat griddles (we have 2 of them in the camper) and an electric skillet. We haven't used the electric skillet in a while though.
The electric griddle is great for pancakes, eggs, bacon sausage patties. But we use it for stakes, ribs, chicken, and chops too. Basically, we use the flat griddles for everything, expect boiling water.
The secret is to find a pan lid that is just the right size to fit on top of the griddle. So when cooking, the lid works as a dome, keeping heat inside, cooking, more like an oven. This also works very well when cooking outside. It keep grease from splattering, and it keeps wind off the food, cooling it before it even has a chance to heat.
Use still occasionally use our propane stove (built in the camper), and we still carry the right equipment we can cook over an open fire (pots, pans, hotdog forks) all the time. You just never know when a power failure may occur since we are always camping with electric hook-ups. The only time we use the propane stove top is for cooking pasta, which requires boiling water, and coffee from an old style non-electric, stove top peculator.
Our griddles are all Presto brands. We have 2 sizes of flat griddles and of course the Presto electric frying pan. The electric adaptors that plug into them with the heat controls work for all 3. So we don't have to worry about keeping track which plug goes with which device.
For what it's worth ... an electric "grill" will also still get messy with splattered grease. You will still have clean-up to do. But the amount of clean up will be determined by how big the grill is.
We gave up the Coleman (gas) flat griddle, that also came with an actual grill because the entire stove would get so greasy, it was just as much a mess to as anything else. And stowing the thing away dirty was NOT an option.
Electric flat griddle is easy to clean. Wipe the grease off with paper towel, and a simple wash, and done.
Besides, when the grease begins to form from the meats and it drips into the drip pan, I always add some butter, let it melt too and drip into the pan, and then use those drippings to constantly baste the meat (pour the grease back over the top of the meat over and over again). Keeping it under the lid, trapping all the heat, constant basting of the juices and ... oh yum!
And oh... the lid for the electric skillet lid fits just perfect on both electric griddles. That's why we keep hanging on to the electric skillet.