Different people here have posted different opinions as to whether or not you'd notice the difference between 32 and 34, but if somebody offers to give you either an 11-32 or an 11-34, take the 11-34, just in case.
Yes. No one who posted about there being no real difference between the 32 or 34 cassette claimed the 34 was not easier. It is. A little bit easier. But the difference in ease is negligible. Probably never notice the difference if you rode both cassettes back to back. Not worth spending money to change the cassette unless you just want to spend money. If you have a free choice, then take the 34 cassette. Assuming your rear derailleur will fit underneath the 34 cog. Some derailleur hangers are sized so the derailleur cannot get under a 34 cog. Just fits under a 32 cog.
The person who posted the question has a 44-32-22 crankset and 11-32 cassette. Assume 9 speed on his Trek 520. The 22x32 low gear is 18.2 gear inches. At 90 rpm he is going 4.9 mph. With a 22x34 low gear the gear inches are 17.1. At 90 rpm he is going 4.6 mph. At 80 rpm he is going 4.3 mph with the 32 cog and 4.1 mph with the 34 cog. 0.2 to 0.3 mph difference. Can you tell the difference?