It might also be a good time to clear up any misconceptions about shapefile precision. If you fail to specify a precision and scale and leave them as the default of 0 and 0 when you select type Double, you get 6 decimal points. You can specify a precision and scale and you pretty well get what you want within the limits of the ability to record coordinates in a 64 bit environment (about 53 bits of information).
So what does that mean?
Well lets do a calculation. I added 2 fields and calculated the X coordinate of a rectangular polygon AND added 0.123456789 to the resultant value. The field on the left was created using a precision and scale of 0 and 0 and I got 6 decimal places, the one on the right was created using a set precision and scale values in an attempt to capture the decimals given. I got 9 decimal points. A millimeter? I would only need 3...we are well beyond that... this is precision NOT accuracy (totally different topic).
Now what does this mean again?
Well, these are real world coordinates in a Modified Transverse Mercator Projection (MTM zone 9 in Canada), the scale factor is 0.9999 for this projection and a zone width of 3 degrees longitude and the units are meters (metres... in Canadian and world spelling). Soooo my coordinates regardless of which field I choose can be represented to way more than I need. In fact, If I wanted to limit the value that would be considered to be equal, I would use a file geodatabase and not a shapefile (see XY resolution, environment settings).
These discussions have a long history so you need not worry about whether one storage system is more precise than the other as is often implied. Shapefiles will be around for a long time, they are a well recognized and used storage format even given their shortcomings. So when you choose a file format to show your data, make sure you have all the facts, understand the pros/cons and limitations of them and ... more importantly ... know the needs of the people that you want to distribute the data to... not everyone in the world uses Arc* products.