Where to start! There are differences and similarities between oils and acrylics and it would take a couple of art lessons to go over all the details. It also depends on how the artist relates to and feels about the different paints.
Here are three things about the paints and I may add more points later but hopefully these give you some good information for starters.
1. Both oil and acrylic paints are made with the exact same pigments - that's the color part of the paint. Pigments are usually in powder form but to become usable as paint those pigments need to be "bound" so that they stick together, can be applied with brushes, can adhere to the paper, board or canvas and can dry to a quality color. For acrylic paints, acrylic mediums are used to bind the colors and oils are used to bind the pigments in oil paints.
2. Artist quality (not student or craft quality) paints of both oils and acrylic are used to make top quality fine art. The colors are basically the same and can have the same brilliance or saturation. Acrylics have not been around long enough to know if they will last for centuries as oils do but I would think they will do very well if they are quality paints and have been used and cared for well.
3. One of the biggest differences between oils and acrylics, at least to me, is the texture. Oils can hold every detail of every brush stroke as the artist lays it on the canvas or board. It will not shrink or loose it's texture as it dries. On the other hand, acrylics will always smooth out a little bit and lose some volume and texture. You can add gels and mediums to the paints to create texture but it never stays exactly the same as when you brushed it on. This means an acrylic painting is often very flat/smooth when dry. (oils can be flat too it depends how they are used, they are flexible.)
I like both mediums and use them for their different characteristics although you can get almost identical results with either. There have been times that I forget whether a painting was done with oils or acrylics and I have to check the back where I labelled them to see!