Some players hear good things about the Vibro-King, try it, and just don't "get it". I have no problem with that - you need to know what's best for your style. I'm hoping this article will give you a bit of insight into what the VK is good at.
I've always been a light-touch/light-strings player. I like to use my picking position and intensity to color the tone. I went through a long (and frustrating) series of other amps that just didn't respond well to my playing - they'd end up being either too sterile or too mushy.
The VK, for me, was the answer to a prayer... It cleans up beautifully without getting dull, and cranks out some gorgeous horn-like tones when I crank the guitar and dig in. Best of all, though, is that I can get lots of shades in between clean and dirty just by changing the way I pluck the strings.
That said, the VK is an odd amp in many ways. A lot of Fender amps obey the 'rule of six' - a good starting point is to set the volume and treble at six, the bass at two and the mid at three (2 x 3 = 6...). That'll work with the VK, but you're gonna have a heck of a time getting a clean tone out of it set like that. The VK has more gain than blackface or silverface amps, and gets dirty quicker than even the old tweed amps.
If you need a really loud, crystalline clean sound, the VK is going to fight you every inch of the way. Strike one: the speakers have a low efficiency and break up early. Strike two: lots of preamp gain. Strike three: no negative feedback in the output stage, so it breaks up early, too.
Of course, all those design decisions are good for something. That something is awesome touch sensitivity.
My technique has changed a lot in the little over a year I've been playing through the VK. I've totally ditched my pick, and now pluck using just my fingers. The pick was too aggressive for the cleaner passages, and didn't let me take advantage of the amp's nuances.
As you can tell, I love the amp and it works well for me. A lot of people flat-out don't like the VK, and that's OK too. But if you're on the fence, I'd like to suggest a few things for you to try.
First, work on your picking-hand technique. Experiment with the different tonal 'colors' you can get by varying picking intensity and position. Likewise, try different pick thicknesses and materials. Try not using a pick.
Second, (especially if you're using a humbucker guitar) lose the notion that all of the guitar's controls have to be full-on all the time. I get some of my best sounds using subtle changes in the balance between the bridge and neck pickups. Also, rolling off the volume at the guitar lets you pick harder (getting some more 'snap') without pushing the amp into distortion.
Third, try lighter-guage strings. A lot of the current obsession with heavy-guage strings comes from players who play aggressively all the time, either for effect or to give their amp that little extra push into its sweet spot. The VK isn't like that - it'll turn to mush if you push it too hard. Let the amp do the work - save your hands.
Fourth, experiment with your pickup height. If you have them set high, you can probably get away with dropping them a bit. This'll help give you more control over the amp, and will open up your guitar's sound a bit.
Fifth, if all else fails, experiment with tube swaps. Try a 5751 or a 12AY7 in V4. They'll help the amp to distort later. The 12AY7 will have more of an effect than the 5751.