The way Apple designs their OS is different. It may stay on a same screen waiting to load for quite some time, but it will not drop a frame for any animation. Apple dedicates a lot of RAM to run just the launcher (in Android term), while Android distributes them evenly.

Apple is also the one to build the OS in and out, so they can push releases extremely fast. The Android equivalent here is the Nexus, where Google builds the OS in and out themselves, push to Nexus right away. Samsung (even though they may have acquired the code earlier before release) will still need to spoil the OS a bit by adding their stuff, so the lag time is always there. At least be appreciative that S4 is among the first of non-Nexus to get 4.2 officially.

So the answer is always, root and custom ROM to get the best out of Android.

Apple's multitasking ability is not as extensive as Android, because it will kill the apps off to reserve enough memory for its core applications. Android gives probably equal loves to most apps (more used apps will get more love still though, with less used apps usually clean off the memory), while there are tricks to keep launcher in memory, there are times we simply see the launcher gets restarted, the phone/contact app loads again everything - all these you don't see in Apple. Apple could pull it off because it's an OS built for a limited number of devices, and for the most parts, they have control over the hardware in the already small pool of devices.

A Nexus comes very close to the smoothness level of iOS, while still enjoying all the extensive features an Android could offer. As Android evolves, it will remains its versatility, and slowly getting smoother and smoother. iOS? I don't see how they get versatility when they dare not give up the smoothness.
That said, within the Android camp, I think the Samsung team probably is the best - they manage to come up so many features, push the quickest updates (apart from Nexus).

EDIT: My last rooted phone is a HTC Desire (yet to itchy to root my current devices), and I can boast it probably is smooth enough to rival the iPhone 4, even if it runs on Gingerbread. So I expect a rooted Android to be able to get the same performance level as the iOS devices, especially Nexus. (Often the times, Android users install Task Manager or RAM Booster and enforce Power Saver mode ALL THE TIME which affects the performance and smoothness. Else I think phones in 2013 should be fine.)

Just look at HTC who struggles with a half-baked BlinkFeed (custom RSS feed yet to come) and Highlight Reel (custom audio yet to come), and ships with 4.1 (out since mid-2012). Don't get me started on Sony, and I think LG has enough reputation to claim themselves the slowpoke in Android.

if you root and remove the bloatware will it be smoother?

S4 no lte?
S4 have snapdragon and exynos version.
In gsm arena snapdragon one say got lte while exynos one market dependent.
Why malaysia s4 no lte? Frequency not match?

It's actually because Samsung wants to push their S4 out early, to fight with One and Z, and probably create enough gap until the next most amazing thing come out from the Apple camp. I believe they only manage to start mass manufacture the Exynos chip, and couldn't get enough time to stock up their inventory and thus have to source from Snapdragon. To sugarcoat their sourcing of Snapdragon (which is because of the delay in the Octa-core), they try to make the Snapdragon LTE-enabled but not for the Exynos. However, the Exynos can do 4G just fine, so some regions still get it in the end.