If I set the same font size in .sublime-theme and in user settings, I get different results.
Here I start ST in safe mode and edit font settings as shown on the picture. The same font settings are used in default theme for tab label. But it is clear that tab label text is smaller.
I’ve tried to play with ui_scale option and with OS scale settings. While they change absolute sizes of text, relative discrepancy stays the same. Issue exists in both ST3 and ST4.
My OS in Windows 10.
No really an issue. Smaller text on tabs, sibebar and the bottom panels are part of the Design.
This is not related to the Design.
The issue is that “font_size” is interpreted differently in settings and theme files, with the same value producing different sized text.
That is part of the design. Smaller labels are part of a visual hierarchy in the User Interface. 
A certain font_size has to result in the same visual size everywhere on the screen on a certain resolution and (dpi).
If the theme would use font_size: 8pt and the editor control `font_size: 11pt by default, it would be by design.
Displaying 8pt smaller in tabs, sidebar, … than in editor, is just a (scaling?) bug.
IIRC, it was already discussed during last dev cycle, but judged rather low priority as it is quite easy to adjust those font sizes to end up with same visual size.