Trying to find a high-speed, high-power transistor to use as a switch

I think you'll need to quantify the current and voltage to get good advice. 10MHz is very fast for typical H bridge type applications.

Do you have  a preference between MOSFETs and BJTs ?

As you probably already know its easy to get high current and high voltage at low speeds and possible to get very high speeds at low voltages and currents - getting all three is very hard.

What is the end game here ?

MK

You might have a look at Gallium Nitride transistors.

They still require a 10-ish ns deadband. 1MHz is just doable for a half bridge.

IGBTs are very slow.  100khz is pushing the limits.10mhz I've never heard of with an IGBT.

You may also consider pre-engineered GaN half-bridge modules or ultrasound pulse drivers.

No real information of what is a high voltage and what current needs to be supported.

You could examine RF power transistors, discrete or otherwise. Here is an example dual transistor (i.e. half a H-bridge so two would be needed for a full H-bridge) which is pretty high-power and high-voltage, with a driver built-in. https://ww1.microchip.com/downloads/en/DeviceDoc/DRF1400_%20B.pdf 

The price is as expected...

Discrete transistors are going to be pricey too. They will come in funny packages, and you may need "opposite-packaged" pairs, otherwise it's a bit hard to route traces for them.

I tested TI LMG5200. GaN half bridge + frontend in a single package. It can switch fast - 1 MHz. Still a magnitude slower than the reqs. 

http://www2.arrl.org/files/file/QEX_Next_Issue/2014/May-Jun_2014/Horowitz.pdf

But .... this is a quasi linear application of an IGBT.

The rise and fall times (of the IGBT they used) add up to 37ns so they wouldn't work in a switching H bridge at anything like 20MHz - might scrape1MHz but they would get warm.

But unless the OP comes back an explains better what they are looking for we are, to coin a phrase, "switching in the dark" (although he did say switching speed, but he might have meant switching frequency which is more commonly measured in Hz)

Has anyone (here on E14) used IGBTs in a linear application.

There is a nice Analogue Devices app note for an audio power amplifier design but you can't buy the P channel parts any more.

I've used IGBTs in linear (high-ish) power regulators with reasonable success.

MK

Vernit was hopeless but I found it on google:) 

Did you try it at 10 MHz

Exciting I will read about your adventure!

Edit: I goofed the search, it is there

No. My board (and TI's ref design) top out at 1 MHz (i forgot it could actually do 10)