Large TIFF files used to be a killer for speed and good performance. Personally I haven't used those for ages since there are better formats out there for large raster files such as ECW.
Large grid files can have some of the same drawbacks as TIFF files as they mostly aren't using pyramiding or other technics to boost the performance.
You don't specify the sizes of your datasets, but Pitney Bowes is working on a new 64-bit product for working with grid and raster. It will be called MapInfo Pro Advanced and it's an add-on for MapInfo Pro similar to Discover and Vertical Mapper.
We do currently have a trial version that you can try out if you want to. Have a look at this article from The MapInfo Pro Monthly Journal: Get on the Grid: A look at the powerful grid coloring capabilities in MapInfo Pro Raster.
In the article you will also find information about how to get a copy of a the trial version.
With MapInfo Pro Advanced we are also introducing a new grid and raster format: MRR, Multi-Resolution Raster. You can read more about this new raster format in this article: Get on the Grid with MapInfo Pro Raster
With this new technology you will not have problems working with large grids; that's grid at +100 GB.