"... I almost always answer 1.e4 with 1...c5, and the move 2.Nf3 is chosen against me in less than half of my games. …" - GM Evgeny Sveshnikov (2014)
Which has more theory to Learn for Black: Classical e5 or Sicilian?
Around 2010, IM John Watson wrote, "... the Sicilian Defence ... almost always means playing with less space and development, and in some cases with exotic and not particularly instructive pawn-structures. ... if you're taking the Sicilian up at [say, 1700 Elo and above], you should put in a lot of serious study time, as well as commit to playing it for a few years. ..."
I would say it depends on the Sicilian variation you plan to head into
I was wondering about the Scheveningen (sp?) variation. ...
"... The advantage of the Scheveningen is that it is much more of a system, rather than just an opening where lots of moves need to be remembered by rote. Therefore general understanding is likely to get you further than in other openings …"
https://www.newinchess.com/media/wysiwyg/product_pdf/7062.pdf
"... The Scheveningen Sicilian, which arises after 1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 e6, was ... once the centerpiece of Kasparov's opening repertoire against 1 e4. Then the Keres Attack, 6 g4, emerged as a somewhat problematic answer and the Scheveningen's popularity faded. …"
https://web.archive.org/web/20140626221508/http://www.chesscafe.com/text/hansen162.pdf

As for memorization vs. understanding.
For your own development it's far more important to think for yourself from the very start.
--- Garry Kasparov, How Life Imitates Chess
Thanks for this quote SoupTime4.
That said, it just pushes the question back one step. Between the Sicilian and 1. ... e5, which one requires the least amount of time to understand?
As a related sidenote, I have read somewhere that at the Club Level, many Sicilian players have to prep their anti-Sicilian repertoire because many 1. e4 players don't want to prep their Open Sicilians. Is that true?
You are asking the wrong person. I am just a casual player, that plays the occasional speed chess game online. The only studying i have done is with those infomercial looking Igor Smirnov courses. I thought i would at least get a set of ginsu knives with a course.
"Dealing with the Anti-Sicilians has never been a trivial task for chess players and writers alike. One has to be ready for a wide spectrum, which varies from boring to surprisingly dangerous, and this diversity is extremely hard to cope with, especially if you are not armed with sound positional knowledge. ..."
https://www.qualitychess.co.uk/ebooks/BeatingtheAnti-Sicilians-excerpt.pdf

We go back to basics:
Choose your favorite player, and study his games, specially annotated games!
Who is your favorite player/players?
"... As I was improving my rating and facing stronger and stronger opposition, I realized that in order to be successful as Black, I needed to play sound but complicated openings, otherwise my winning chances would be close to zero. After a lot of deliberation and experimentation, I concluded that 1.e4 e5 would be an ideal choice. ..."
https://www.qualitychess.co.uk/ebooks/Playing1e4e5-excerpt.pdf

As for memorization vs. understanding.
That said, it just pushes the question back one step. Between the Sicilian and 1. ... e5, which one requires the least amount of time to understand?
As a related sidenote, I have read somewhere that at the Club Level, many Sicilian players have to prep their anti-Sicilian repertoire because many 1. e4 players don't want to prep their Open Sicilians. Is that true?
The least amount of time? It depends on the systems and the opponents you'll be playing against. But it can be said that the lesser the need to be up-to-date in critical opening lines, the higher the need to understand the system in the long term, which generally requires more time.
An example. Decades ago, I was talking to a strong NM (an IM strength by nowadays standards) who was telling me he wasted time studying the Sicilian Najdorf because all the lines he learned, back in the '60s and '70s, were obsolete at that moment (early '90s). Which was true. The systems he played were based on fast counterplay and recipes were discovered for White, so sometimes he lost to 1st cat. players just because they were aware of the latest theory. I also used to play critical lines in the Sicilian, but as I'm not a competitive player anymore nowadays I play long-term counterplay systems, meaning I avoid critical lines and play instead on the understanding of the available long-term plans for both sides. And I can't complain, at least not as the NM used to.

We go back to basics:
Choose your favorite player, and study his games, specially annotated games!
Who is your favorite player/players?
In my youth I would have reflexively said Bobby Fischer. Now, I'm not so sure.
With all the good counsel provided so far (thank you everyone!) I will opt for 1. ... e5.

Play the Modern Defense against everything. Soltis covered it well about 20 years ago, with a couple of books. Tiger Hillarp Persson covers it well in two books written over the past 5-10 years. You can use one system, against everything white can play. Very simple -- IF you want to keep your opening study to a minimum, AND it puts most of your opponents on unfamiliar territory.
Openings are largely a matter or taste. Lots of folks buy tons of Opening Books that end up collecting dust on their bookshelves. That's what I did for nearly a decade. But no more.
Hellsten and Nunn write great books on the other two phases of the game. That kind of study is much more interesting, and rewarding too.

Well, if it is 1...e5, you have a lot of good players that you can study. To name a few:
Zukertort, Rubinstein, Lasker, Keres......

And if you want to drive yourself mad, and down the rabbit hole of endless, endless theory. Yes, play the Sicilian, (or the KID). And your study will never end. It's all a matter of taste, and how much time you're willing to burn.

The least amount of time? It depends on the systems and the opponents you'll be playing against. But it can be said that the lesser the need to be up-to-date in critical opening lines, the higher the need to understand the system in the long term, which generally requires more time.
Hey, hey, hey!! No fair. No giving away with one hand, and then taking away with the other!

528 pages.....all games commented, not only by Zukertort, but by players like Steinitz and Chigorin! Worth every penny!

Bronstein's recommendation on how to study....
"You should not "read" a chess creation but you should move the pieces on the chessboard and make move by move exactly as the work of Chess Art was created for the very first time. On your own chessboard with your own chess pieces and in complete silence, to be able to follow closely the events as they unfold before your very eyes. The best way is to do this in three stages."
"First, play through the whole game without hesitating more than a couple of seconds at each move. If you have the urge to pause longer-don't! Take a piece of paper and make some notes if you wish, and continue to play the game to the end. Then get a cup of tea or coffee, relax and try your best to recall from memory the spectacle you have just seen. Try to establish the reasons why certain decisions were made."
"Second, play through the game again, somewhat slower this time,and make notes of everything that you did not see the first time."
"Third, now go straight to those pencil marks and give your imaginative and creative energy free reign. Try to play better than my partner and I. If you do not agree, look closely at each decision, either for White or for Black, with a critical eye. If you look at a game like this you will discover a lot of new and useful knowledge, which you can use for your own benefit."
"Write your findings in a notebook in order to look at them later when you are in a different mood, especially if you like the game. If, during stage one, you took no notes, don't look at this game again. Go on to the next one that, hopefully, will give you more pleasure and satisfaction. It just means that it did not appeal to you. Although I consider chess an Art, I will not blame you at all if you do not like a particular game. In a museum you cannot like every painting you see. As French gourmets say, taste is a very personal matter."
"When I was learning to play chess, I studied thousands and thousands of games played by the older generation in exactly the same way and gained a lot from them."

Some great books are available for pennies...a great book about Lasker is available for as little as $3.00!
https://www.amazon.com/gp/offer-listing/0486267067/ref=sr_1_2?keywords=Lasker+Chess&qid=1585092994&sr=8-2

Your're a mind reader, Zeitnot17.
Yes, play black defensive systems with the white pieces. I do that too. And there's So Much Time Left Over -- to study the rest of the Royal Game.

And a book with 100 Selected Games by Rubinstein, also available for $3.00.....
https://www.amazon.com/gp/offer-listing/0486206173/ref=sr_1_3?s=books&keywords=Rubinstein+Chess&qid=1585093289&sr=1-3
As for memorization vs. understanding.
For your own development it's far more important to think for yourself from the very start.
--- Garry Kasparov, How Life Imitates Chess
Thanks for this quote SoupTime4.
That said, it just pushes the question back one step. Between the Sicilian and 1. ... e5, which one requires the least amount of time to understand?
As a related sidenote, I have read somewhere that at the Club Level, many Sicilian players have to prep their anti-Sicilian repertoire because many 1. e4 players don't want to prep their Open Sicilians. Is that true?