Personally I prefer broad advancement for my characters. I like to be flexible, and find that this approach lends more to that in play. The tricky bit for a system is to be broad or detailed enough that you can have a party of broad characters without them all seeming cookie-cutter in nature. GURPS addresses that by having so many options PCs can have different approaches to the same challenge, hence feeling different while being able to operate in a similar space.
Trying to play a more broad character in a strongly tall system like D&D means I end up playing almost exclusively bards or wizards. Wizards are arguably the most flexible class since their load-out of spells can be tailored to be more tall or broad on a daily basis. Trying to be broad in a tall system has its own challenges, however. Tall systems tend to have scaling difficulties to keep challenging the players. That can make broad characters who, by definition, aren’t specialising in one thing become basically irrelevant. There is almost no benefit in being second best at picking locks, for example. Or even the social skills - the Face character will always be the character the party want to talk to NPCs by default. These issues can be overcome by more nuanced GMing (e.g. making more use of languages, or encouraging the party to split up) but basic scenarios pretty much fall into the trap of only needing one character to be good at a a thing.
Fully broad systems can end up being a min-max exercise, GURPS certainly falls into that trap a lot of the time in my experience. Some kind of limit is desirable, like in Hero. I particularly like how Savage Worlds handles this, with caps on various skills and edges based on your stats and/or your rank. It is functionally a broad system with no classes but don’t-call-them-levels.

I think that is an overall positive for the system. Savage Worlds offers a decent balance of tall vs broad through encouraging a broadening of skills via the cap system while offering vertical growth through chains of edges. You tend to see characters specialising in a particular edge-chain for their main schtick while they still gain a degree of breadth. The system also helps by having a useful system for helping other PCs - you really can play a fully non-combat character and still contribute in fights by applying knowledge or social skills to help/hinder as appropriate. Dramatic Tasks encourage group solutions to non-combat encounters, too.