I like to have both on the camera, so when holding in hand I can use the wrist strap and ignore the big strap, but when I need to park the camera temporarily I use the big strap, either on my shoulder, or around my neck when I need more security. Then if I have a small bag for more protection, say, going into an eatery and keeping the food off of the camera, the camera strap can act as the bag strap for ultimate convenience. But that's one camera - if I use a small camera or carry both cameras, I might move things around. Which is why quick-removal straps are very convenient.
Been using the default leather strap that came with the box, but it already showed some age and some peeling on the outer layer where the strap lugs are... so just to be safe, I'm using an Artisan and Artist strap now.
I attach my straps to a carabiner and that allows me to quickly change the strap i have. Or, i wrap a strap such as the A&A cloth neck strap around my hand. Barton straps are very nice. I use a wrist strap when I am walking the streets shooting and a neck strap if walking in the countryside
I like Riley G designworks. The thinner "Dapper" ones with their "superloops". I also have a Tapestry one but it is a little too thick for my taste.. certainly good for a heavier camera. High quality. Comfortable. Not boring. Sued underneath so it doesn't slide off my shoulders.