This is a very complex issue. All amps sound a bit different so it is hard to say which pair of solid state and tube amp sound alike. Among very high end amplifiers, I tend to find that solid state amps sound quite similar to each other while tube amps tend to vary much more in sound. Overall, I like low-powered tube amps the most and have not found any solid state amp that I prefer over a number of such tube amps. The good low-powered tube amps have a very natural sound -- rich in harmonics, realistic attack and decay of notes, enveloping soundfield, very lively and engaging sound at low volume levels. Even very good solid state gear tends to be a touch lifeless sounding at lower volume levels. Solid state does deliver very tight and impactful bass. I don't like many high-powered tube amps because of a brittle or harsh quality to the sound. Thus, it is really hard to say what, if any, two amps, one solid state the other tube sound alike.
At best, I can say that I like some solid state amps regardless of whether they sound like any particular tube amp. While I haven't heard their newer models, I liked older Ayre solid state electronics. I also liked a couple of First Watt amps I heard. I heard a SIT-3 in a friend's system and I had a J-2 First Watt amp in my system for a couple of weeks. They are both lively sounding amps that don't suffer from being lifeless at lower volume levels.