The logo on basis looks very small

You're right, the logo doesn't display very big. Depending on the site, it's however a good fit, in my opinion. See an example of my test site:

If you want your logo bigger, you could override the corresponding CSS rules, e.g. from core/themes/basis/css/component/header.css:

.header-logo-tall img {
width: auto;
height: 100%;
}

and maybe also from core/themes/basis/css/base.css:

img {
    max-width: 100%;
    height: auto;
}

I suppose you can add another CSS code:

img.header-logo {
width: 200px;
height: auto;
}

I am nut sure what is CSS selector in your case - img.header-logo or other but with correct CSS selector that rule should work.

And in "width" put the desired real width in pixels or % of parent block element width. This can be changed in responsive css rules for different screen sizes.