That's a matter of opinion. There's no mechanical reason one way or the other, so it's purely a matter of aesthetics. If you like the backsplash, use it. If not, don't. :-)

Will that be any water/wet issue if no backsplash? Should I have countertop installed first and the do the tile or do the tile and then do the coutertop? My stone vendor seems like to have countertop installed first and do the tile but general contractor thinks other way.

-J

Caulk the tile to the countertop, and you'll be all set. Doesn't matter which goes first.

I had a lot of trouble with this decision in my self-designed bathroom. My advice is find a photo of a vanity top with a backsplash to see the difference. Pick the photo of the setup you like best and print/save it to show your contractor or tile shop or countertop fabricator exactly what you want. On the site Houzz dot com with decorating photo examples (thousands!) from designers I see that the modern designer look is not 4 inch countertop backsplash. Now I see another reason vessel sinks are so popular--they eliminate the need for the counterop backsplash/sidesplash. Here are photos I saved when I started my remodel to try to pick the way I wanted mine to be.

The thread discussion on Houzz that I link below has a lot of photos of this to compare.

[contemporary bathroom design[(https://www.houzz.com/photos/contemporary-bathroom-ideas-phbr1-bp~t_712~s_2103)

Here is a link that might be useful: [countertops and double sink vanities[(https://www.houzz.com/magazine/double-sinks-a-relationship-saver-stsetivw-vs~75400)