There are solid state amps that can make a sound stage as good as a tube amp, but most of them are class D.
The differences you hear between tubes and traditional solid state has been about distortion for the last 60 years. Solid state amps have higher ordered harmonic distortion that is more audible than that of tubes, and so tend to be bright. They also can have more distortion at lower power levels, and that can mess with low level detail. But on paper, they appear to have less distortion. But 'less' should be taken with a grain of salt, since the ear reacts differently depending on the kind of distortion being produced.
This stuff is pretty audible; its measurable too but understanding what the measurements mean, and more importantly getting the right measurements is a bit of a trick. One trick that is used commonly in audio is to measure the distortion of the amplifier at 100 Hz. Any solid state amp will measure well at this frequency. But the problem is that such amps have feedback to control distortion, which goes down as frequency increases, because the Gain Bandwidth Product on which the feedback relies is insufficient. So distortion rises with frequency. That is why its measured at 100 Hz, to cover up this problem.
The has been going on for so long that many people, including people that test amplifiers, don't think of it as a problem. But if you measure that amplifier at 3KHz things start to look different- you can see how its distortion is increasing.
So you have two ways to avoid this- either no feedback at all, or so much feedback that the amp is able to compensate for the distortion added due to the operation of the feedback. Feedback does this, if in **insufficient** amounts, through a process called 'bifurcation'. When there's **enough** feedback, this process is suppressed. But that takes north of 35dB, and traditionally to do that at 8-15KHz hasn't really been possible with most of the semiconductors available to designers in past decades. So we still have tubes, which are fairly linear even with no feedback, although they will make more 2nd and/or 3rd harmonic.
The lower ordered harmonics, the 2nd, 3rd and 4th, get treated by the ear the same way- they add a little 'bloom' or 'warmth' (audiophile terms for this) which is relatively innocuous compared to the higher orders, to which the ear is keenly sensitive. If the 2nd or 3rd is present in enough quantity, it will mask the presence of the higher orders and the amp will sound smooth. They also allow you to hear a greater perception of the sound stage- this is the part that most people don't get. The better class D amps have a similar distortion signature (although at a much lower level than tubes, but nevertheless mostly lower orders) and so they can sound quite tube-like (i.e. musical), including the wider deeper soundstage.
The thing is, you might think this to be an error of amps like this, but if you've had the opportunity to hear what the actual musical performance sounded like, you find out that its helpful, because in this way despite the distortion, the sound stage is presented much closer to the original than amps that don't have this property!