There´s is a number of reasons why W was so popular, i am not exactly a fan of the show, personally i prefer OOO, but even though it didn´t clicked with as it did with others i can see why so many people like it. From an objective perspective the show had a perfect balance between characters, comedy, plot, action and villains. I guess you could say that the show was perfectly executed.
That said, i think that one of the main reasons why W was such a success was because of how straightforward it is.
Looking back a the previous seasons, Decade was an anniversary show, Kiva had the two time periods gimmick, Den-O had the time traveling trains and the whole "possesion" thing, and all the previous seasons had this Dorama quality to them, well, except for Hibiki but that is another beast entirely.
Looking at that precedent is easy to see how W´s Style was such a lump of fresh air, the show had simple premise (an unussual detective agency that deals with humans transformed into monsters) and a cool gimmick (the Gaia Memories). Sure, there was a lot more to the show than that but the simple premise and format of the show made it quite accessible, almost anyone can jump in and watch this "Kamen Rider" thing and enjoy it right away.
This is a quality that was somewhat lost in the following seasons, i love OOO but i have to admit that the show is not easy to get into, or at least not as easy as W was. While the Dopants were just humans that transformed for some selfish reason, the Yummies were manifestations of desire, not to mention that the greeeds are a complex bunch. Basically the approach of OOO is more complicated that the one of W, and while Fourze is quite an entertaining show, you have to admit that the premise and its execution are a tad bizarre.
Now, when it comes to Super Sentai, i guess we can all agree that entire point of the franchise is having a group of people and seeing what they can achieve together. This, i think, is the determining factor of Shinkenger´s success.
From the moment it started, Shinkenger had this likeable cast of characters, they were all unique in their own way and none of them felt half-assed. The show made these characters the main focus and this enhanced all the other elements of the show, the plot was interesting, the side stories were interesting, heck, even the villains were more interesting, and this is particularly important because since these villains were such a genuine threat you cared even more about your main characters.
Basically the show had many good qualities and the characters just rounded it up and made it all special. For comparison take Goseiger, the main concepts and the plot of the show weren´t bad, but the main cast was so lame that everything became lackluster.