A tie or a 'World's Best Dad' mug are the default Father's Day gifts in the US. The default is fine but it is also the same gift he has gotten for years.
When a tie is still right. Recipients who actively wear ties at work. Specific colorway or fabric he has mentioned wanting. Pairings (a tie plus a smaller picked gift) where the tie is not carrying the whole weight.
When a tie is not enough. Dads who have not worn a tie since the last family wedding. Dads who work in tech, manufacturing, or anything where ties are not part of the dress code. Recipients who have explicitly said 'no more ties' (believe them).
When a mug is still right. Recipients who actually drink coffee or tea and have a small mug rotation. Mugs from small ceramic studios with real character. Pairings (a mug plus a coffee bag).
When a mug is not enough. Recipients who already own ten mugs. Anything labeled 'World's Best Dad' or 'Dad of the Year.' Mass-produced novelty mugs that crack within a year.
The upgrade. Skip the generic tie and mug entirely for a small consumable he will actually use: a small-batch coffee bag, a single-origin chocolate bar, a BBQ rub. Same price, much better hit rate.
The pairing. If you must include a tie or mug, pair it with a much smaller specific consumable and a handwritten card naming three things you appreciate about him. The card outperforms either object in long-term recall by a wide margin.
What to avoid. Same-day novelty Father's Day bundles from chain retailers; the markup pays for the photography. Mugs with one-line jokes you will not find funny in 18 months. Anything that arrives on Monday after Father's Day; it reads as worse than nothing arriving Sunday.