Should I peel my tomatoes before making a sauce? What are the pros and cons of peeling my tomatoes before making a sauce?

I basically make two different sauces a classical red sauce and a "pink" sauce that is a light alfredo infused with white wine and then chopped tomatoes are added and reduced.  

When making my pink sauce you can see some skin afterwards but not much and most people like the texture.  However I am talking to a local chef and we are picking tomatoes in his back yard and he tells me he skins them all... I have never had issues but ???

Note:  I am getting a lot of feedback and I think there may be confusion.  I chop my tomatoes into relative small cubes (let's say 1/3" cubed).  There isn't much trace of skins and those left are very small slivers.  Also is skin on vs skin off affecting taste?  People love my pink sauce so I don't want to change the taste.
It is unnecessary, however some people don't like the skins. They tend to curl up into tube sticks that don't chew very well and can hurt if you chew one accidentally and you have a sensitive tooth or gum disease.

Peeling it very easy. Score an x at the bottom of each tomatoe and blanch. The skin will curl back and leave you with a whole but peeled tomato.

Edit based on change to question:
The skins will have almost no affect to the taste either way.