Either, Or. I think both could look nice. I went with a 4" counter backsplash and am very happy with it. Sometimes the tile backsplash can look good and sometimes it looks like an after thought. I know the difference when I see it in a picture, but right now I can't describe the difference. I don't think you can go wrong with a 4" counter backsplash and it would keep things tidy at the sink. I keep a small white microfiber cloth at the faucet to wipe things down after I splash around :)

In my area I didn't want the added element of tile. I was going for several large areas of interest and nothing more. I have a bold floor, a bold vanity and contrasting counter. I didn't want another element by using a tile backsplash.

With tile like that, I'd take it to the counter. I think if you put it above the 4", it would look like it was added later. But it wouldn't bother me, I think you'll have a nice result either way.

Just use the tile. If you're worried about cleaning grout in a mosaic, and I would be, use a row of ceramic tile at the counter. I think a design like these from Houzz really elevates the mosaic into a special treatment. I also like when only one or two rows of mosaic is used. I love mosaic but I prefer it in moderation for a backsplash and shower accent.

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[Traditional Bathroom[(https://www.houzz.com/photos/traditional-bathroom-ideas-phbr1-bp~t_712~s_2107) by Denver Kitchen & Bath Designers Elizabeth P. Lord Residential Design

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[Contemporary Bathroom[(https://www.houzz.com/photos/contemporary-bathroom-ideas-phbr1-bp~t_712~s_2103) by Irvine Interior Designers & Decorators Serendipite Designs

Thank you both for the input. I picture the tile going all the way down (so no counter backsplash) i think I'll stick with that thought. I did a 4inch bs in the kitchen and never really liked it (I have a tile backsplash too)

may_flowers - I think we both posted at the same time - I'm just seeing your comments and pictures - I love your idea and have never thought about that before!! I'll have to find some ceramic or porcelain tiles - to put in the mix - thank you :)

With the contemporary feel of your glass mosaic and quartz, you'll want to avoid the chunky top molding tile in my examples. Look for tile like this or something even more clean and simple. I do like the inch of white tile above the mosaic versus capping the mosaic with a thin molding.

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[Traditional Bathroom[(https://www.houzz.com/photos/traditional-bathroom-ideas-phbr1-bp~t_712~s_2107) by Washington Design-Build Firms Four Brothers LLC

Not as much of a fan of the cap here.

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[Traditional Bathroom[(https://www.houzz.com/photos/traditional-bathroom-ideas-phbr1-bp~t_712~s_2107) by Burnsville Design-Build Firms Highmark Builders

Actually, the molding in the second photo with the long gray vanity is a pretty good size. Love the white tile above it. I wonder why they posted the photo to Houzz before installing the mirrors.

You could also use a Schluter edge with the mosaic if you can't find a molding that works.
This is how it looks in my daughters bathroom.