Integrated tube amp vs Tube amp?

Usually the amp is powering speakers, and the speaker impedance comes into play at some point.
If they are super sensitive, then don’t bother with the amp… IMO.

What is the sensitivity and impedance profile (or rated and minimum ohms)?
That will help as a way to provide some useful recommendations.

For instance, if it is those big Moab’s, then get a big class-D.

I am using McIntosh 302 amp now. I wanted to experience “tube” sound and was thinking of trying “horn” sound also by getting a pair of Klipsch Cornwall 4 s. Currently have Goldenear Triton 1s and Ohm 5 Mk2s.

In most cases, I would say yes - you'll get more performance from a pure tube amp. Tube integrated amps often have very simplistic preamp & volume stages in order to fit into the same box & budget. Simplistic is fine, but...if you hear an ARC Reference 6 or VAC Master, you will know what a big box pre can do (neither of these will come close to fitting into an integrated). The power amp section of an integrated could also be compromised a little for those reasons. Having to use an extra set of interconnects sucks, but still worth it imo. 

The biggest stopper to most people going to separates is having to buy 2 components up front instead of one - but you've already got the preamp. Go for the tube power! You'll also gain more flexibility down the road - sometimes the brand-matching pre & power aren't actually the best sonic match in your system, to your ears.

I am using McIntosh 302 amp now. I wanted to experience “tube” sound and was thinking of trying “horn” sound also by getting a pair of Klipsch Cornwall 4 s. Currently have Goldenear Triton 1s and Ohm 5 Mk2s.

I suppose you can choose speakers based upon the amp, or the amp based upon the speakers.

At this point thinking about whether you want an integrated amp or stereo amp, or monoblocks seems a bit premature… IMO.

What is wrong with the golden ear or the Ohm speakers? Or what can be improved on?

There are 2 schools of thought on preamps:  Preamp should "add to sound quality" and "preamp should be invisible".  

Integrated tube amps usually are looking for the 2nd path to success.  So if you're in that school of thought, integrated tube amps may be the way for you to go.

If you're in the first school, then separates may be the way to go.

Jerry