The earliest transistors were the "point contact" type, and made on a base of germanium rather than the silicon which everybody associates with transistors these days. Semiconductor diodes were made the same way, not really dissimilar to the "cat's whisker and crystal" diodes which had been in use as radio detectors for many years. It was a little later that "junction" diodes and transistors appeared to eliminate the cat's whisker approach, although the point-contact transistor still had certain advantages over junction types for some applications.
The vacuum tube and the bipolar transistor do indeed have very different operating characteristics which require something a different approach to design and servicing. The tube, for example, is an inherently high-impedance device, whereas the transistor operated with much lower impedances. Even the polarities of DC voltages and currents could be off-putting. Many of earlier transistors were the PNP type, which means that the main supply rail is NEGATIVE. Engineers used to years of dealing with tube circuits with POSITIVE B+ supplies suddenly had to start thinking about all the supply, biasing, etc. polarities in a circuit in reverse.
Somewhat ironically, the field-effect transistor which was developed some years later actually has characteristics which more closely match those of tubes in many ways.
In the early days, transistors were suitable for low power applications at relatively low frequencies. They could handle neither high frequencies nor high powers effectively.
It's easy for people nowadays to think of the transistor as heralding the space age, for example, and without the low-power consumption and miniaturization of transistors, some of the early satellite projects such as Telstar would have been impossible. Yet at the same time, those projects could not possibly have worked without the continued use of thermionic devices, such as the TWT (Traveling Wave Tube) used to provide the high power signals for transmission at the extremely high frequencies involved. Transistors at that time were simply not capable of providing the power needed at those frequencies.
In domestic equipment, TV sets employed tubes well into the 1970s, and even the early 1980s in some cases. Hybrid sets gradually became quite common from the 1960s onward, with transistors being used in the small signal stages (I.F. amplifiers, AGC circuits, sync separator, etc.) and tubes for the parts of the circuit which demanded higher power (line output, frame output, final video amplifier, etc.) or, in the early days, which had to handle high frequencies (e.g. the UHF tuner).
And of course, the thermionic tube never really went away completely even after all those high-power stages became transistorized, for the cathode-ray tube itself is just a special type of vacuum tube.