If a BMW has a Ford Cobra 500 hp engine installed in it, will it drive better, faster, or what?
Switching tube is more than matching the voltages. Just because it fits in the socket doesn't mean it will work.
A KT120 or KT150 has a lot more 'horsepower' than a KT88. If the amp you have is designed for X watt output and you now have X+2 or X+3 power tubes in it, you may well be over driving the output transformer and or demanding more 'juice' from the power supply that it can supply. Both of these situations will not be ear pleasant.
Some mention that they can not get the bias pots to the desired mv reading when switching from KT88 to KT120 or KT150. If you can not, then your tube is burning COLD and while that may make the tube last for 10 or 20 years it sounds ....cold, may even sound buzzy, and is running towards class B, or more simply to 'cut-off' of the power. Not being able to bias to the recommended point (unless something is damaged) means that amp is not designed for that high an output.