I've never played SW, but I've GM'ed it a bit... one-shots and a few short campaigns. D&D, I've played extensively and GM'ed a fair bit... but mostly in in Basic and 2e, with a little bit of 3e. Never 4e/5e though.
Mechanically, they are pretty different. There are a few token similarities, although it kinda depends on which edition of D&D you are comparing against. Obviously, D&D is a class and level based system. SW has levels, and it kinda emulates classes through Professional Edges -- which are basically a mini-package of abilities, sometimes offset with some disadvantages. It's not exactly the same, but does allow players to create 'archetypes' if that's their thing. Races are kinda similar to Professional Edges -- they are a package of abilities, typically offset with some disadvantages. Edges, though, are generally akin to 3e feats. Because skills are fairly flat and there isn't a huge skill list, characters can end up (mechanically speaking) being fairly similar and Edges can be a pretty important differentiator. If you are suffering PTSD from D&D 3E and all the splatbooks with new Feats, then SW might bring back some uncomfortable memories.
IMHO, the really big difference though, is between the feel of the systems. A typical SW character starts out pretty competent, whereas a D&D character (at least, from the earlier editions) is typically pretty weak. But herein lies the real issue... because IMHO, everyone's D&D experiences are different. I played Basic D&D in the late 80s and we (theoretically) played the rules as written. In practice, though, the DM regularly fudged dice rolls and threw us softball encounters because otherwise, we would have been TPK'd on numerous occasions. And we used max HP for the first few levels. The old-school rules could be tough and the first few levels could be a real grind. But then again, I knew of a few groups that started at 3rd level and regularly found magic items and consumables... so I dare say their experiences were pretty different to mine.
I suspect the appeal of SW to D&D grognards is that it's "rules medium", with reasonably solid, tactical combat. It doesn't put a huge emphasis on social skills and non-combat actions, but has just enough rules to cover them. This means that good roleplayers can fill in the blanks themselves, and good rollplayers can just get on with rolling dice. You're generally not going to be confronted with anything warm-and-fuzzy in the game, like more modern, indie games offer. It's also pretty hackable, so if the swashbuckling style doesn't suit you, there are more than a few ways to make the game more gritty. If classic D&D means to you, things like equipment lists with rope, lanterns and a 10 foot pole, and tracking encumbrance... you can definitely do this in SW.
For a fantasy game, it's magic system is pretty boring, and doesn't emulate D&D at all. But I'm basing this off the core rules... there might be some flavorsome magic systems in some of the 3rd-party supplements. But I like my fantasy settings to be pretty low-magic, so it's never really bothered me.