Is 433Mhz TR slow?

I am using 433Mhz TR for my project -

I noticed that my transceiver application spends around 170ms to send 20 bytes message. I use RadioHead library with default settings.

Is it expected performance?

Will 2.4GHz transceiver be faster -

Yeah, OOK transmitters are slow as hell, that's expected.

It's not the frequency that determines that, but the modulation scheme and sophistication of the hardware. OOK is pretty primitive, and the hardware is garbage too (those are the crappy kind of receivers too - not that radiohead will recognize and take advantage of nicer OOK transmitter or receiver modules; I don't use that so I don't know if they have an option to increase the speed if you're using nicer receiver and transmitter).

the NRF24's are probably better, but I think they're still fairly slow. Neither of these are meant for high speed.

Could you recommend affordable module with the better speed? Will wifi or Blue tooth work faster?

nRF24's only operate at 2.4GHz, the comparable hardware for the VHF ISM bands are devices like the
RFM12 and RFM22. These can be configured over a wide range of baudrates and FM deviations and
are actually tunable too.

The nRF24's support 3 baud rates only, 250k, 1M and 2M, they are plenty fast, but the range is of course
pathetic at 2.4GHz compared to 433MHz. Expect 10 feet or so indoors, especially if there
are microwave ovens or WiFi in the building...

Range depends on quality of the transceiver, quality of the antenna, antenna alignment, baud rate (slower
has more range), and most importantly on the wavelength (larger wavelength has larger range unless
beam antennas are used - a beam antenna has to be clear of obstacles and permanently mounted pointing
in the right direct, often not feasible).