Apparently, in terms of design, the formal shoe is always meant to look quite simple and elegant, for instance, a black cap-toe oxford for your every formal attire.
However, in terms of formality, the shoes will be categorised according to the design elements of the shoes, therefore, the brogues would be placed in between the formal and casual styles of shoes.
What is broguing and where is it came from?
Obviously, it's a sort of design part which is perforated and with serrated edges on the upper, also it originated in the Irland and Scotland, although it's traditionally considered an outdoor/ country shoe; therefore, the perforations were purposely created to allow the upper to dry quickly in the monsoon season.
Although, brogues have various types, such as full brogue/ wingtip, semi-brogue/ half brogue, and quarter brogue.
The full brogue/ wingtip: the entire upper portion (toe cap, vamp, facing, and heel cap ) will be decorated by the perforation and with serrated edges and especially the toe has been designed like a wing also the beautiful medallion design on the toe which is called the toe medallion.
Semi-brogue/half brogue: the decorative perforations appear on the straight edge toe cap and the quarter (the mid portion of the shoe), facing and on the heel cap.
The quarter brogue: the decorative perforations that only appeared on the straight edge toe cap.
Whether it can be a full brogue, wing tip/ semi-brogue, or half brogue/ quarter brogue despite it would be significantly distinguished in terms of formality, therefore, you can't wear them with your tuxedo and even particular formal attire.
How to style
The versatility and timeless look of the brogue shoes would give a nice compliment to your most of outfits; which means you could wear them with your everyday office outfit and also with your semi-formal, casual outfits as well.
Whether it might be a suit or perhaps odd trousers with a blazer/ sport coat, besides the cotton trousers/ chinos with sport coat/ denim jacket, and denim jeans with a shawl collar cardigan/ sport coat/ denim jacket.
However, personally, I would prefer a dark brown wingtip/ full brogue derby shoe with dark-wash denim jeans, or chinos with a brown suede jacket or a sport coat, and black, burgundy, oxblood, a semi-brogue oxford shoes with odd trousers along with a blazer or sport coat.
Eventually, a black, dark brown, or oxblood, quarter brogue/ semi-brogue (as a second option) oxford shoe with a suit to add a bit more flair and an exuberant look.
Cheers gentleman