Thanks to @Gr8pimpin for the recommendation, we decided to try out Joe’s to see how it compared to Ta-Eem (and Tel Aviv Grill). 
This had been on my bookmark list for a while but I forgot about it until the reminder.
Joe’s is an interesting place in that unlike Ta-Eem or Tel Aviv, it focuses on more than one cuisine. When I asked the server, they mentioned “We are a Greek Israeli restaurant.”
Looking at the menu of Tabouleh, Baba Ghanoush, Gyros and even Lamb Shank over Rice (I was looking for some Ghormeh Sabzi at this point LOL), and you can see it’s more diverse than the other places (and maybe not as focused).
Chicken Shawarma Plate:
The actual Chicken Shawarma is dryish (it seems @Gr8pimpin was talking about the Chicken Kabobs, but then it’s not a fair comparison with Ta-Eem at this point (they don’t serve Kabobs), but like @Ns1 @Bigmouth mentioned, there’s some nice crisped skin / edges which makes it appealing. It was pretty tasty.
1 Salad:
However, after that the rest of the offering was disappointing. It comes with 1 Salad (and not even an Israeli Salad), just some mediocre, semi-limp Romaine Lettuce and unripe Tomatoes in a generic Vinaigrette. 
Compare that to Tel Aviv Grill’s bountiful (4 - 6 Israeli Salads), or Ta-Eem’s absolutely delicious array of Israeli Salads (they are delicious on their own - Curried Carrots, Red Cabbage Salad, etc.), and this is woefully disappointing.
Their Hummus was fine. Creamy, semi-thick.
The Pita was warm, but dryish. Tel Aviv Grill’s Pita is far better, and Ta-Eem’s is even better than that (slightly toasty on the outside) and both of them are fluffy, airy and outstanding. Definitely better than Joe’s.
Joe’s also only gives you 1 Pita per order, and charges you $0.75 for each additional Pita (vs. Ta-Eem’s 4 (amazing) Pitas and additional ones for Free).
Falafel Pita:
It’s kind of hard to see here, but Joe’s Falafel Pita is pretty sparse and only about 40% - 50% of the size of Ta-Eem’s or Tel Aviv’s.
It is also filled with just some Tomatoes and the semi-limp Romaine Lettuce.
However the Falafel itself is wonderful! 
It is what @Gr8pimpin @Ns1 have said: Definitely the crunchiest out of all of the places. So if you like crunchy Falafel, Joe’s is the best of the bunch. The inside is still moist, and it’s nicely spiced (although we didn’t get any heat).
Price-wise, Joe’s is the cheapest of the bunch: Joe’s Chicken Shawarma Plate is $10.25 (vs. $16.95 (Ta-Eem) / $14.95 (Tel Aviv)). And Joe’s Falafel Pita is $5.95 (vs. $7.95 (at both Ta-Eem and Tel Aviv Grill)). However, portion-wise, it feels almost like only 50% of the size of Ta-Eem or Tel Aviv.
If you’re looking for just pure crunchy crust and the Falafel alone, Joe’s Falafel is the crunchiest and tastiest of the bunch, and their Chicken Shawarma has the most crunchy edges. However it comes up short in too many other ways: It’s not Glatt Kosher (this matters to many of my Jewish friends). Its side accompaniments consists of just 1 limp Romaine Lettuce Salad, whereas Tel Aviv Grill and Ta-Eem’s Israeli Salad array are a meal unto themselves (let alone the fantastic Roasted Eggplant (for free)), and really make a difference elevating both places’ dishes.
The Pitas are so far superior at Ta-Eem and Tel Aviv (they are paradigm changing tastes - so fluffy, airy, warm, tasty), compared to Joe’s. And there’s no Housemade Skhug or Harissa Sauce which are stunning at Ta-Eem Grill. And it’s like half the portion.
Ultimately while it might seem I’m down on Joe’s, we really liked it for the delicious Falafel and Shawarma. It’s a nice place for the price if we were in the neighborhood. But when we want to eat Falafel and Shawarma, the additional accompaniments really matter, as does the base (Pita), and so we’d tend to favor Ta-Eem and Tel Aviv.
Joe’s Falafel
3535 Cahuenga Blvd West
Los Angeles, CA 90068
Tel: (323) 512-4447