I never played a lot of 3rd Strike so I can't make a good comparison, but I do agree that I never quite got the SFII comparison either having bought SFIV not long after getting the Super Turbo HD Remix and playing then both quite a bit at around the same time. There are quite a few aspects like focus attacks which are pretty fundamental to the game which weren't in II. Not to mention I agree that it felt quite a bit slower, not to mention quite a bit more convoluted than SFII with multiple meters and moves that are sometimes needlessly complex.
Some of the things that its similar and why i say so is in bulletpoints:

-Throws are LP+LK and not one button. Similarly, Taunts are also the same set of buttons.
-Focus Attacks are kind of a ghetto Parry.
-EX Moves started from the SFIII series.
-Super flash animation ripped straight from SFIII
-The ability to choose Ultras is very akin to choosing Super Arts from SFIII.

The only thing similar is that fireballs aren't negated by Parry straight out for some spacing, but even then theres many EX moves or moves that go through them. The reason i say this is because HDR and the original SFII relied heavily on positioning and fireballs are a key part of it. Its not as key to SFIV as they were in SFII thats for sure.

I am pretty confident that the comparison was purely for marketing on our nostalgia because outside of the original characters being there, the gameplay is surprisingly not very SFII.

On thate note, i really love the original game <3 It has a great charm to it even after all these years.