I can think of some positives for both, but I lean more towards a website feature, namely for a few social/community reasons.
I think it’d be cool to be able to integrate it with player profiles, for example being able to have various builds listed and visible on your account (if you wished). You could have a search function for builds of a certain class, with filters for skills or uniques utilised. I’m sure there are plenty of other things that having it integrated with the site could allow, those are just some random things that come to mind.
I’m a fan of how https://www.diablofans.com/builds for D3 works, where you can search and filter builds, make comments and vote on them (separate from the forums, which I personally don’t find well suited to sharing builds). When you are looking at someones profile it’s easy to find all their builds, how popular they are, when they were updated and what they are about. It’s the sort of thing I always wished the official site had, as opposed to the bare-bones Skill Calculator that’s there. It hasn’t aged very gracefully and you guys could do it so much better, but the general idea is there.
You could do some of that with a program by sharing links/import code, but I don’t think it’d be as seamless or as user friendly. Then there’s the issue of storage (local or cloud) and making sure you’re using the most up to date version of the program. I imagine that could get complicated for developers and users alike.
Part of the reason I mentioned PoB isn’t so much because it’s a program, but more so because of its functionality, which is extensive and goes beyond what a typical build planner usually has. If you can get the functionality and features you want out of a site (whatever that may be), I think there’s no need for a downloadable program.
A tool like PoB is a different beast entirely really, and isn’t something that the average player will get a lot of use out of, unless they are making their own optimised builds or theorycrafting. Personally, I’d like and use it, but I don’t think it’d be the right approach if the goal is to help members of the community engage more.
tl;dr It really depends what the goal of this is…With a website feature you could have a robust search and filter system that will be more user friendly and aide in community engagement.