Trying to put the smaller width hub onto your wider frame will probably answer your question.

Sometimes it works and sometimes it doesn't. I tried it recently and found that the small sprocket hit the rear stay, ending my hopes to use that particular wheel on that particular bike.

The biggest problem is probably the head-ache of the wheel not fitting correctly when you need to do some kind of roadside repair like fixing a flat. When you are home with all your tools, maybe even the wife to hold the wheel while you knuckle bust and curse, everything is so-so O.K.

When you are alone on the side of the road with ants crawling up your shorts and the asphalt cooking your shins, you will be swearing in languages you never heard of before.