I started off with the MS-DOS version, and to be honest, I find the controls in the PlayStation port to be pretty intuitive - I can't imagine any way that they could have been done better...
(Not only that, but, rare as it is, they're fully redefinable if you don't like any of the alternate options, either.)
Anyway, I would imagine that much of the footage on YouTube is not an accurate representation, as it's often taken from emulators. Running the MS-DOS version of Lemmings 3D in DOSBox, for example, usually results in something that runs *MUCH* faster than it really did on hardware of its time. Not only that, but I know that there are some Lemmings 3D videos that show up if you search YouTube for footage of the Saturn version, which are actually of the MS-DOS version (one of them mentions this in the description).
Having run the MS-DOS version on a contemporary PC of that time (the game was bundled with the first x86 box that my family got, in fact; The machine was equipped with a Pentium 75-level CPU, 8MB of RAM, a 1GB hard disk drive, and ran the first revision of Microsoft Windows 95), in reality it originally ran about the same as the PlayStation version does. The loading times were pretty similar, too - and it's a shame to note that the lemmings who appeared on the loading screens, holding the word "LOADING" in the Lemmings font, are absent in the PSX and Saturn versions.
As a point of note, the MS-DOS and PlayStation versions were coded by the same company (Clockwork Games), whilst the Saturn version was not (it was handled by Perfect Entertainment, instead), so I'd have expected far more differences between the MS-DOS and PSX originals, next to the third-party Saturn port, myself.
Also;
Slow loading times is a consequence of the games running off of CDs I think. I don't remember but I think the DOS version makes you install the whole game onto your hard drive, right?
As far as I remember, it didn't, no. It just saved your settings to the HDD.