Update:
Thanks to the reminder from @A5KOBE, we stopped by Fugetsu-Do in Little Tokyo, to see how the oldest of the Japanese Confectioneries in L.A. compared. Founded in 1903(!), walking in to Fugetsu-Do had a charming, old-timey feel to the place. 
Current owner and Mochi maker Brian Kito represents the 3rd generation of the family that has been running Fugetsu-Do since his grandfather Seiichi Kito opened it up in Little Tokyo in 1903.
We ordered 8 of the most enticing looking Mochi / Manju on display:
Green Tea Manju:
Manju is usually made with Flour, Rice Powder and with a filling of Red Bean (or White Bean), and we were intrigued (I love Green Tea!). The Manju was just OK. It tasted like a denser, chewier version of Dim Sum’s Charsiu Bao, like a Steamed Bun. The filling had a slight Green Tea tinge, but really was very sweet from the Red Bean.
Ume Manju:
This was Manju that supposedly had Ume (Japanese Plum) mixed in with the Red Bean, which sounded wild. This was also hampered by the dryish, dense Manju outside, but the Plum mixture - slightly tart - helped balance out the Sweetened Red Bean filling a bit.
Red Bean Daifuku:
This is like Mochi but it’s chewier, with the focus on the pounded Rice. The Sweetened Red Bean filling however was really sweet. It was nice, and slightly chewier than the standard Mochi.
Kusa (Red Bean) Mochi:
Their classic Mochi (with Sweetened Red Bean) has a delicate, soft texture, with the rice exterior being more pliant and not as chewy as the Daifuku.
But in terms of delicate, pillowy-ness, Sakura-Ya is by far better, with Fugetsu-Do 2nd, and Chikara Mochi 3rd.
Kiku (White Bean) Mochi:
The White Bean filling is also just as over-sweet as the Red Bean at Fugetsu-Do. Our friends didn’t mind, but I felt in terms of Sugar content, Sakura-Ya was less sweet (better), with Chikara Mochi 2nd and Fugetsu-Do 3rd.
Habutai (Red Bean) Mochi:
This was their classic Mochi with Sweetened Red Bean, with the white rice exterior. It tasted pretty close to the Kusa.
Uguisu (Red Bean) with Kinako Mochi:
This is their take on the Toasted Soy Bean Powder Mochi. While the Kinako was wonderful, their overly sweet filling detracted from the Mochi for us.
Strawberry Anco Mochi:
While it’s spelled “Anco” on their display, this is essentially their Anko (Red Bean) filling which is much smoother than their chunkier version in some of the Mochi.
It is also a newer fusion flavor, catering to the younger generation perhaps, with a real Strawberry Jam-like taste, mixed in with the Anko itself. It was different, kinda fun, but also a bit too sweet.
One of the nicest aspects is what @A5KOBE mentions about their gift-wrapping. They feature Free Gift Wrapping when you buy their Mochi, and it’s definitely the nicest presentation out of all 3 places (to give as gifts):
Ranging from $1.25 - $1.50 for each sweet, Fugetsu-Do is right in line with the other 2 places.
In thinking back on all 3 Confectioneries now, I’d have to say:
Taste:
- Sakura-Ya
- Chikara Mochi
- Fugetsu-Do
Sakura-Ya has the perfect combination of amazing pillowy, cloud-like fluffiness, and is less sweet than the other 2 places, especially their White Bean filling. That combination makes the overall taste our favorite. Fugetsu-Do would’ve been 2nd if they used less Sugar, but it was just too sweet for us.
Texture:
- Sakura-Ya
- Fugetsu-Do
- Chikara Mochi
Just in terms of pounded rice, softness and feel, Sakura-Ya is first, and Fugetsu-Do was better than Chikara.
Visual Artistry (“Plating”):
- Chikara Mochi
- Fugetsu-Do
- Sakura-Ya
Just visually, Chikara has the most beautiful, creative, fun Mochi to wow yourself and friends & family. Fugetsu-Do has some interesting looking ones as well, but also has plain ones. Sakura-Ya may not have the pretty exterior, but they more than make up for it in overall Taste & Texture.
Variety / Flavors:
- Fugetsu-Do
- Chikara Mochi
- Sakura-Ya
Fugetsu-Do had the most varieties & offerings (they also had a Blueberry-flavored Mochi(!), besides the other flavors like Green Tea and Ume). However, we felt that they were undermined by the excessive Sugar content in their fillings. 
But ultimately, all 3 places are much better than the typical “Mochi” you might find prepackaged in supermarkets, etc.They are wonderful places to visit when you get a chance.
Fugetsu-Do
315 E. 1st St.
Los Angeles, CA 90012
Tel: (213) 625-8595
http://www.fugetsu-do.com/
Or you could try this: 
