HoI3 predates the current DLC policy (and it actually has a couple of dozen if you include all the graphical packs, etc.).
A few really important differences:
- HoI 3 has several different scenarios throughout the 1930s and 1940s; HoI4 assumes you'll start in 1936 (1939 is an option, but you'll miss out on many features).
- HoI 3 has a complex order of battle system that you have to set up before play can really start. It's great to be able to give roles to all of your favourite generals, but I'm told that setting up Germany or the USSR takes hours.
- HoI 3 is slow throughout, especially since it can only use one CPU core. HoI 4 slows down once combat starts, but it's fairly speedy until then and was designed to use multiple cores.
- HoI 4 has a production system based around building equipment for your armies, which makes for a really interesting trade-off between introducing new equipment and keeping factories running efficiently. HoI 3 has a more complex research system, which also provides lots of flavour texts about components.
- HoI 3's air war uses individual squadrons that must be moved with lots of clicks; HoI 4's air war is more geographically abstracted
- Espionage is only represented in outline in HoI 4 (this will probably be fixed in a patch+DLC sometime)
- HoI 3 allows you to switch almost every element of the game over to the AI and you will have a LOT of clicking & pausing if you don't use the AI at all in a major country, so it requires similar timeframes to CK2 & EU4 to complete a game. HoI 4 almost requires you to use the AI to manage some tactical placement, but everything else is up to you. People with sufficiently powerful computers can and do complete games in an evening (not my style, but it's very popular in the multiplayer world).
And obviously HoI 3 isn't getting bugfixes anymore & doesn't have much of (any?) multiplayer community, while HoI 4 is under active development so things might get changed (usually for the better).