This question is a decade old, but still highly trafficked, so I figured it's worth adding my (more recent) insight as a PCB designer by trade (U.S.-based).
Background
At this point, mils/inches are starting to feel somewhat obsolete for a handful of reasons:
- All new SMT footprints are defined in metric. Routing in mm allows for slightly more optimized fanouts between pads (not super relevant at low density)
- Most off-the-shelf enclosures are specced in mm (especially true if you are 3D printing one)
- All IPC guidelines are in mm, as well as any new IEEE/IEC/JEDEC/etc specifications for package, connectors, etc
- Ucamco (creator/maintainer of the Gerber format) has made it clear that mils/inches are deprecated and will be eventually be removed from the Gerber standard (worth noting though that this doesn't actively affect routing in mils, they round to the nearest nm just fine)
- All new equipment related to assembly, and almost all new equipment related to fabrication, is configured and operates in metric, often without the ability to change
- All FCC/CISPR/NRTL testing (or any sort of post production verification) uses metric exclusively
- The standard board thickness has moved from 62mils (1.57 mm) to 1.6 mm, even at board houses that still primarily use mils for traces. And even those that do still spec in mils have a perfectly competent understanding of mm.
- Ounces are now just a placeholder, copper thickness is controlled to the micron (oz/ft2 has always been a silly unit for people who don't make the foil)
Grid
If you are looking for your board to be compatible with all output formats, everywhere, then a 0.05 mm grid (or its multiples) is technically the objectively correct answer, as it's been agreed upon by dozens of organizations and will work without rounding for all outputs.
However, we're at a point where you can pretty much throw grids out the window unless you're going for visual appeal. Gerber X2 recommends 10nm or 1nm grids for all outputs, small enough that any routing grid is huge by comparison. When I'm doing HDL I usually place on a 0.05 mm grid (for assembly) then route with grid off since it serves little purpose.
That being said - if your components are aligned on a metric grid than your a routing grid can actually be useful (that is, a 0.1mm placement and routing grid means your tracks will connect perfectly with most newer component footprints, and go exactly between vias for BGAs).
Summary
In short, if you're seasoned at designing and used to mils, there's really not much motivation to change (though I was, and I did), especially on the hobby level. And everyone should certainly use what they are comfortable with. However, if you're just starting out, my recommendation at this point would be to learn to route in metric. 10 years ago I would have said it really doesn't matter, but the industry (currently a messy mix of both units) is slowly but surely moving toward metric only, so it's worth at least getting a feel for that.
Exceptions
For completeness, here are few exceptions I can think of:
- U.S. based dielectric manufactures use an annoying mix of units. Not critical for hobby level but mildly irritating for high speed boards
- Many U.S. boardhouses will still give you overall board dimensions or stackups in inches on drawings, even if they communicate in mm. That's just old software, shouldn't affect how you design your board
- 0.1" / 0.05" connectors, are still out there en masse (in addition to DIPs and 1.27mm SOIC), but this is hardly relevant when modern components have much smaller pitches
- Some datasheets still give trace length / matching specs in mils, though most list both and some list mm only. (Not relevant for hobbiests)