One area where golfers do need to pay a lot of attention to compression is around the green. Lower compression balls will feel softer and will generally spin more. So if you are around the green and you're faced with a very tricky shot maybe of a tight lie where you need to stop it quickly next to the pin, having an eye softball will definitely fill you with much more confidence. If you're looking to test out how a low compression ball may react versus a high compression ball around the green please do a very, very simple test.
Get yourself maybe a box of three of these balls each, so low compression versus a high compression golf ball. And then go to around the green and then pick yourself a regular chip shot of about 20 to 30 yards where you need a sand wedge to land it on the green before it checks and then releases out towards the pin. Now hit the shots alternately. Hit the low compression and then hit the high compression ball and see if you can notice the difference between the feel and how it reacts on the surface because this goes hand in hand with what you want to see with the rest of your game. Softer feeling balls around the green will give you a greater sense of touch, but they should and maybe will go the less distance off the tee, but like I mentioned this is not always the case.
So you need to avail the options. Can you control a higher compression golf ball around the green or is a lower compression golf ball something you need to be paying attention to, to give you the added touch around the plotting surface. As always this is not for me to decide. This is for you to get these balls and test them out and see what you will find when you start to hit these shots around the green.