Pros of acrylics - Acrylics dry fast, which can be important in a living area. Acrylics are water washable which is a huge plus when you are painting and possibly spill on floors, clothes, your hair or skin, etc. Acrylics leave a faintly plastic texture, especially with higher gloss content, which can be nicely washable when things are spilled or dripped on the acrylic surfaces. They're often recommended for higher traffic areas like kitchens, doorways, and kid's rooms because of that wash ability. Because of the plastic like texture, acrylics can expand with or contract with the item they are painted on when these movements occur due to heat, moisture, or weather. Acrylics allow moisture vapor to escape which helps to prevent blistering or flaking, especially important when painting woods. They are also generally mildew and fungus resistant, which can be helpful in a bathroom or outdoor area. They're generally cheaper to buy than oils and you don't need any special cleaning or storage solutions or solvents.

Cons of acrylics - If you layer them too fast they get clumpy and sticky. You generally need to paint smaller areas at a time. While they do dry "quickly" compared to oil, you really have to be sure each layer is dry before adding the next. And because of the quick semi-dry feature, you can't blend them as well if you want to use them for faux painting. They can become "tacky" that is sticky to the touch in moist climates and in some situations that exterior moisture can lead to the "plastic-like" coating that is part of acrylic to also peel like a plastic coating. Thus in a bathroom that is not well ventilated, you could get some peeling.

Pros of oils - Oils (enamel paint) are generally a lot longer lasting than acrylic. They form a hard shell over the surface they're painted on and are thus very durable. Many of the old "classic" homes that still have their original paint are painted with oil based enamel paints. You can lightly sand dings in oil paints more easily than in acrylics because the hard shell layer sands easier and doesn't gum up, which can make it easier to repair nicks and scratches.

Cons of oils - Oils don't allow for moisture escape, which can cause buckling and peeling if they're on a surface like wood that needs to breathe. The hard shell like finish doesn't allow for flexibility on any surface that may swell or contract with different temperature changes, thus it will buckle and peel if the surface under it moves. The brushes need to be stored in an airtight container if they're not completely free of paint, and they need to be cleaned off with a solvent. If they drip on the floor or your clothing or skin, don't plan on removing them easily if at all. They take longer to dry. They also emit flammable fumes so no smoking while painting!