I've been thinking about these two for a long time and I wanted to see what others think.
I know it's going to sound crazy, but please bear with me.

My general opinion from playing is that Athletics is superior to Acrobatics most of the time, and especially for Rogues.
So much so, I've been thinking that a Rogue might be better off taking Expertise in Athletics and leaving Acrobatics off their skilled list.

My reasons are this:
Athletics covers extensively what I consider are rogue-ish things: climbing, jumping, etc... most of what I call "Jackie Chaning around".
Acrobatics on the other hand is keeping your balance and not falling on your butt.

Here is my point, a Rogue already has good Dex and so will already have a good chance of not falling on their butt, but Rogues usually have low strength and so putting Expertise into Athletics will mean the Rogue will actually be as good at this as if they had a high stat.

See Math Below: 

My thought being that while Acrobatics or Athletics are both a defensive stat, when it comes to resisting Shoves/Grapples/etc...
I think Athletics is actually the superior stat and worth considering taking over Acrobatics on a Rogue even if it's counter intuitive because a Strength is not a primary ability of a Rogue.
My thoughts being that because Rogue are not naturally good at Athletics that's precisely why the skill should be picked up over Acrobatics, because it's a useful skill that probably will be used by a Rogue a lot.

As you can see from the above math while it doesn't make Athletics superior to Acrobatics at lvl 1-4, it makes it competitively equal, the Expertise bonus over takes it with each tier of play.

Side note: Thank you for whoever moved this!
I meant to put it in Rogue, and clicked on Sorcerer accidentally.  It's better off here.

Well it depends on the DM.

If the DM let's you use EITHER Acrobatics OR Athletics to beat a grapple/ climb a wall/ dodge a shove then getting the one that suits your build is best.

If your DM says Acrobatics can't be used to climb or stop a grapple or shove, Athletics would help you be more rounded

I myself am of the mind that a high-dex build should be able to slip a shove or grapple and nimbly climb a wall and that a high strength build will use brute force and power to do the same thing.

So I'd let them use whichever.

I've never had an issue using Acrobats to defend against a Shove/Grapple as it's RAW, but Acrobatics can't initiated a grapple.
I've never been able to use Acrobatics to climb, that's always firmly been a Athletics thing.

The only time I've seen Acrobatics come up is with a balance check. That said, it technically does include things like tumbling, cart wheels, etc. Acrobatics is great if you're walking over a rope over a chasm, or you want to perform by doing cartwheels or other circus acts.  

That said?  I find that most rogues aren't the old school Thief-Acrobats. Of course, the thief subclass is, but the others?  Assassins, arcane tricksters, masterminds, etc aren't necessarily going to be  "Jackie Chaning around." They have different styles of play.

I absolutely agree that Athletics is better than acrobatics, what you didn't mention above is the opportunity cost for your expertise. What more chiefly rogue things could that expertise be put into? I'd prefer to put that expertise into perception or deception or something else. It's not that athletics is a bad choice, but I think the only real advantage for a rogue is in the climbing. In combat, a rogue should almost never use their one attack (and possible sneak attack) to grapple/shove. Not that I don't love grappling, I just think it should be left to fighters and barbarians. I guess the summary here is that I think acrobatics proficiency is good enough for rogues.

As has been said before, a lot depends on the DM. In my game the enemy will play to THEIR strengths so a big, burly enemy may try to pin down a slippery one. I would allow Acrobatics to AVOID a Grapple and even to initiate one but on the subsequent turn, when the bad guy is trying to escape, that's Athletics or simply a Strength check.

All of my Rogues and Rangers take Athletics for the ease of climbing if nothing else. A clever player will often find ways to use his skills even if the situation doesn't seem to call for it as long as the DM is not running the game on the rails. 

Quote from Darkaiser >>

As has been said before, a lot depends on the DM. In my game the enemy will play to THEIR strengths so a big, burly enemy may try to pin down a slippery one. I would allow Acrobatics to AVOID a Grapple and even to initiate one but on the subsequent turn, when the bad guy is trying to escape, that's Athletics or simply a Strength check.

All of my Rogues and Rangers take Athletics for the ease of climbing if nothing else. A clever player will often find ways to use his skills even if the situation doesn't seem to call for it as long as the DM is not running the game on the rails. 

I play mostly Adventures League so the DM isn't allowed to house rule like that. Acrobatics or athletics for avoiding/escaping a grapple/shove and only athletics to initiate one. Given my stance on grappling without extra attack, I think the only benefit to a rogue taking athletics in lieu of acrobatics is climbing.

Have you ever climbed a wall? I promise it's an athletics check.

This is min-maxing, but I tend to take Athletics when I have a high Dexterity score and Acrobatics when I have a high Strength score to balance the two abilities out. Both abilities have their uses so when I’m playing a physical character instead of a spell caster I try to make sure that I have a bonus in both of them. The trade off is my characters are never great at one or the other, they’re only Ok at both.