The main thing to watch with switching high voltages with transistors is that the high voltage portion of your circuit and the low voltage portion are physically coupled. If the transistor should develop a fault there is a good chance the high voltage would be pumped right through the rest of your circuit, and BANG goes everything.
An SSR is isolated by incorporating an opto-isolator, so if there is a fault there is no electrical path between the two parts of the circuit, so there will be no bang.
There are IGBTs (Isolated Gate Bipolar Transistors) which are basically a MOSFET driving a BJT, which provides a better level of isolation than a plain BJT, and are used when very high voltages are being switch (thousands of volts), but still aren't completely isolated.
I'd stick to SSRs personally for high voltage work. Less risky.