A rather old report admittedly, but I changed the basing of my War of 1812 collection a few years ago from thin irregular shaped stands to thick square bases. Originally I believed that the irregular shaped bases 'blended' into the table top making the stands less obvious and showing the miniatures in a natural environment. However, I had based up some AWI French to match Kevin's style and found, after much musing, why I would like those rather than the 1812 versions I placed beside them? Well, I guess it was the uniformity of shape and the very thickness of the MDF laser cut wood.
Darn. Now I would need to re-base literally hundreds of stands. And I needed to order hundreds. Bugger. But for the most part I could, with minimal trimming put the 1.5 inch stands onto the new 40mm squares. It took a good long time but I think the effort was worth my new affinity for this collection.
Obviously I like thick bases, some don't. But in the end it is but one's own hobby and the gain we get from what we like.
Here are the before, during, and after photos from doing one of the units.
Admittedly these photos of these Upper Canadian Militia were taken on a rather bright greenish cloth which forms my on-the-dining-room-table protection than the matching terrain mat I have on the gaming table but one's units could be plunked down on any various terrain so the effect should be the same.