As Maxdimitro pointed out the is absolutely no compression about those two type of tubes....
But let's go a bit deeper than just rumors or propaganda data still floating around from the times when the electron tubes was roaming the electronic world....
For people that do not like it to technical, do not read any further.
Here are some historic infos we have to take into account to understand the difference triode vs. pentode.
In germany the pentode, beampower tetrode and related tubes like heptodes, octodes, etc. were widely used and developed in greater numbers than the better, less noisy and microphonic triodes.
There was a reason for it, in germany everything was taxed to Kingdome come, especially around the "Kaisers" time when the electron tube was developed and started to change our lives forever; the german Kaiser taxed everything from salt to champagne, to fuel his spendy lifestyle and WWI...
One of those taxes were amid at home entertainment, more specific, the tax of a radio receiver was issued by the amount of tubes...
So nearly four month later after law passed (1915), the first tetrode (a prestage of the pentode) was developed at Siemens by Werner Schottky, that did the job of two triodes...
At about the same time GE developed their first version of the tetrode...
Siemens specificly developed the tetrode to avoid a higher tax, were GE engineers worked to get a higher gain amplifier...
The radio tax was not changed before the fall of the 3rd Reich, so all development form 1915 to 1945 was biased by this great idea of the Kaiser....
Following that Germany became the land of specialty audio pentodes, like the RE084, EF12, EF14, EF40, EF804/806, EF86, EF8010, etc. etc. For every developed triode there were about 4 pentodes, the last tube ever to be developed by Telefunken was a Pentode, the EL3010...
From the begging of the pentode age, and even to today there are hard headed people that bring arguments over arguments what sounds better triode or pentode.... (a short side info: the most wanted tube on this globe is the VF14, a pentode followed by a 300B, a triode; that should say it all)
First my compassion is not triode vs. pentode, that does not work, but an amplifier stage with the same gain powered by either one pentode or two triodes (to get the same amount of gain), in this case a EF804(S) vs. an ECC83 (a double triode in one glass container) and later an ECC803s....
To be continued...