How does the Vibro-King compare to a tweed or blackface Fender amp?
On the "tweed to blackface" continuum, the VK is kind of in-between. That's a tough one to explain since the tweed amps went through so many changes in their tone stacks. You have the the tweed Deluxe with its treble boost/cut control, the high-power Twin and the Bassman with their Marshallesque tone stacks, and some really oddball designs like the stack in the low-power Twin. Low power supply voltages contributed to a darker sound and low headroom. Also, the various phase-inverter designs had a big effect on the headroom of the tweed amps; some of the earlier PIs contributed to early breakup.
The blackface amps went toward a cleaner sound by raising the supply voltage, using a high-headroom PI and scooping the mids. The latter change was especially significant since most of the guitar's energy is in the midrange; cutting those frequencies causes the amp to be less susceptible to distortion.
Now the Vibro-King is an interesting hybrid. It puts two gain stages ahead of the tone stack. If you have a guitar with hot pickups you're going to have to worry about the preamp distorting. Any pickups having approximately vintage output levels shouldn't be a problem. You can still scoop the mids, but the tone is a bit warmer because the VK's second preamp stage is being hit harder than it would be in a blackface amp.
The VK's tone stack is pretty close to what you'd find in a blackface amp, with the addition of a filter to cut low frequencies. You don't have to worry about the VK "farting out"; the bass control is actually usable over most of its range unlike on a blackface amp.
The output end of the VK has one significant difference: there's no negative feedback, so you're really hearing the tubes when you play quietly. The VK doesn't need to be cranked to sound good; it has an extremely broad "sweet spot".
The VK is a very "fast" amp. Because it has a solid-state rectifier, there's no detectable sag. You say "jump", it jumps!
Finally, the speakers contribute their own breakup as you start to push the amp. When you push the VK hard it can sound quite horn-like; I think a lot of that has to do with the preamp, the power amp and the speakers all distorting at once. Also, the speakers are relatively inefficient; they're about 3 to 6 dB down from a "typical" modern guitar speaker, so you need to take that into consideration when you think of the VK as a 60-watt amp. A VK's cranked stage volume is probably comparable to a 30-watt amp with modern high-efficiency speakers.
I don't think you'll have any problem getting a good "jazz" tone out of a VK unless you're going for the bass-heavy thumpy flatwound sound; the VK might color your intended tone too much if that's what you expect to hear. In that case, I'd suggest the Custom Dual Professional (no longer in production) or even the Jazz King.
There's certainly no problem covering the blues territory with this amp. Fans of SRV's flat-out playing style and big cleans might want to consider an amp with more headroom, such as the `64 Vibroverb Custom.
The tone controls cover a wide range of good sounds; chances are good that you'll be able to get close to what you want to hear.