Tube amps tend to have a "warmer" tone with nice low mids. Tubes also slightly compress a signal so they may produce a "smoother" tone. Tubes may also bring out harmonics more than solid state. The downside to tube amps is weight and heat.
Solid state amps will be much lighter and may give you better deep lows but you may not have some of the rich overtones that tubes bring out.
A good tradeoff that gives you good tone with light weight is to use a tube preamp with a solid state power amp. The tube preamp will give the "tube sound" to the signal. There are also many preamps that offer both tube and solid state sections that you can blend (that would give you the harmonics of tubes and the deep low end punch of solid state).