Honestly. Whats the difference on some of the older mugs? Also, do you make the lather IN the mug, or simply use it to hold the soap? If its IN the mug, I can see the advantage of the bowl for "whipping" it up.
I have some Old Spice mugs I use just to hold the soap. I load my brush, then take it to a lather bowl and whip it up there.
Since I face lather exclusively, just about anything will work to hold the soap. I use the Anchor bowls from Walmart.
When I first started wet shaving, I had one puck of VDH in a coffee cup, the small coffee cup that comes in the boxed sets of dishes, I guess they are about 6 ounce cups. The coffee cup worked okay, but a large latte cup worked even better. Then I acquired 15 or 20 more soaps and started storing the soaps in smaller stacking coffee cups because I took up lathering in a scuttle.
I like to build lather in a larger bowl, like a small soup bowl with a handle or a latte cup like Jeff mentioned. Coffee cups are ok for storing soaps, but a bit small even for that. As for antique soap/lather cups having smaller diameters, I've always thought of them as more decorative than practical. My granddad may have thought differently.
Shaving mugs are for shaving soaps coffee cups are for coffee. Coffee cups seem too small to use effectively . Most of the old shaving mugs you can find on ebay are 3 ,1/2 inches by 3 1/2, a few are 4 inches . They work because there is ample room to load your brush from the soap and the soap fits snugly in the mug. Old barbershop mugs on ebay are very practical as they are very sturdy and heavier than the old home use mugs. My guess is that vintage shaving mugs are underutilized by wetshavers. Hazel Atlas milk glass mugs can be found for a dollar and many old mugs are $10 or so. Old Spice mugs are nice and wide 3 1/2 by 2 1/2. They work well . I do not find that soaps stored in mugs deteriorate to any great degree. I like the William Marvy green rubber mug , found at barber supply houses online . They are about $10, 4'' by 4'' , unbreakable, sturdy and can accomodate a small puck which fits in the cylinder at the bottom or larger pucks like MWF or the Conk superbar which sits on top the cylinder and higher up in the mug.
I started using a couple of coffee mugs for Williams and VdH soap. I used the mug to load my brush, and built the lather directly on my face. Worked just fine. If I wanted to build the lather in the mug, that would be something different. Later, I got some Old Spice mugs, just because I like them as collectibles. They work fine also, but wouldn't have been worth the extra money except that I just like having them. Got some other old shaving mugs too. Some shaving mugs have ridges or protrusions inside to hold the soap in place, but this really isn't necessary. My last Old Spice mug has a puck of original Old Spice soap in it. I'm now done with buying mugs and soaps for some time, but I couldn't pass up that last deal.
Some ebay sellers are selling Old Spice shaving mugs that actually are coffee mugs. It was an Old Spice promo years ago and most ebay sellers don't know the difference. The Old Spice shaving mug I have has a height of 2.5 inches. Coffee mugs tend to be taller. I can lather in a shaving mug just fine but would have a tough time with a coffee mug. Having said that, I admit I normally move to a lather bowl after loading the brush. What I call a "lather bowl" is nothing special, a dip bowl I got at Target for ~$3. I'm sure similar can be found at big lots, various dollar stores etc.
Flogging a dead horse, perhaps, but . . . I have used all of the mugs pictured below to hold soap pucks while I swirl the brush on them to get it loaded with soap. Again, I actually build the lather directly on my face. The blue mug is the coffee mug that I used when I started. The tallest Old Spice mug was probably intended as a coffee mug, but works fine for me as a shave mug. The next one is definitely a shaving mug, and the one on the right might have been intended as either, but I'm going to guess shave mug. Anyway, they've all worked for me. I have two other Old Spice mugs, and a couple of other shaving mugs.
Spot On. You will go through the soap at a much faster rate. I'd take the grooved bowl of my scuttle over an old mug any day.