To me, proficiency suggests long hours of time and practice; expertise means even more of both. In 5th edition, proficiency only increases a character's chance of success by 10%. Let's take a musical instrument as an example--this says that a character proficient at playing the lute is only 10% more likely at playing a song on a lute than a character who has absolutely no experience with a lute. That holds true for the first four levels of the character at which point the chance of success increases by an additional 5%.
At the highest level (level 20), that character's proficiency is only worth a 25% increase to the chance of success--and that assumes that both characters have the same basic ability score. In 3rd edition, a character who put a rank every level into a skill would be two times more likely to be successful at a that skill rather than only a 1/4th better chance. The difference is staggering, especially for a player (such as myself) who likes to play skill based characters.
There are times that I would prefer to forego the "simplicity" of 5th edition and return back to playing 3rd edition (especially my 3.6 homebrew version). Unfortunately, I only know a couple of people up here who have that rule set. In the end, I prefer to get to play something rather than not play at all.