Either hand can be written quickly enough for daily handwriting. Of the two, Round Hand is potentially the more rapid and definitely more rapid in its monoline or business writing form (no shades). Where Italic has an advantage is in portability. Where shaded Round Hand, as in the example, is more easily and effectively done with dip pens, Italic can be done quite well with a fountain pen.
Or, if you are more particular than you are accurate like me, you'll spend a long time writing whatever way you choose, so pick one you like.
Unless I'm using a flexible nib (on a fountain pen or with a dip pen), my cursive is rotten: I need the directional feedback of the nib to guide me. When I have to use a stiff, smooth nib, or if I'm stuck with a ballpoint, I revert to my semi-cursive italic handwriting. It may be a little bit slower for me, but at least it's legible.
If you want a more-or-less standard roundhand-derived cursive handwriting (including, say, Spencerian or Palmer), I will defer to others to guide you. But if you want an italic handwriting:
In general, if you like stub nibs or italic (or chisel-point) nibs, italic is a good choice for a handwriting. If you want an italic handwriting, you can certainly use a mono-width nib, but my reflex as a teacher would be that learning with a chisel nib helps to learn why
certain shapes work the way they do. I have an Article In Progress™ about this very topic, and will spare you. In any case, my handwriting usually settles on italic, and my better examples of cursive usually use italic letter shapes as a base.