Whether data should be stored and processed in raster or vector form has historically been a source of much debate. The debate is perhaps dying down slightly because most systems, at least from a user's perspective, have some provision for handling both. It is still true that not all operations are supported in both-typical systems compute buffer zones around vector features by converting to the raster domain and back.
Raster has many advantages including simplicity of concepts and algorithms, and hardware support. Remotely-sensed data, displayed output, and many digital elevation maps (DEMs) are in raster form. It is good for data that should be sampled evenly. Rasters are huge, do not scale well, and introduce aliasing effects.
Vector data is natural for linear features such as roads and boundaries, and mandatory for accuracy in instances of land survey. The speed of vector computation is most often criticized; geometers should rejoice in this as an opportunity to provide significant improvements. We should remember, however, that these improvements will need to be realizable for ``typical data'' and will need to provide some feature that raster processing does not provide. Paper descriptions of worst-case optimal algorithms do not constitute significant improvement in a community that wants implementations of solutions.