There are a number of very clear parallels between Tokyo Mew Mew and Sailor Moon, beyond the fact that they're both magical girl animes. At 7:35 of this, the scene is incredibly similar to this at 00:53:10. There are other very striking similarities, like the personalities of the characters. Have the creators of either series commented on the similarities?
Unfortunately the second link you provided has been removed from YouTube so I could not look at it, but based on watching the Tokyo Mew Mew link you provided I can guess which scene from Sailor Moon you’re thinking of. The scenes are indeed similar.
However, the creators of the series would not need to comment on the similarity because Sailor Moon pioneered the genre of team fighting mahou shoujo (magical girl) series. The key point here is the combination of sentai (team fighting) with mahou shoujo. To merely say Sailor Moon and Tokyo Mew Mew are from the same genre and for the same target audience doesn't nearly explain their large similarities, because neither look much at all like any of the mahou shoujo series that preceded Sailor Moon.
Before Sailor Moon, the long history of mahou shoujo series were usually EITHER one girl who could transform into a magical version of herself OR one magical girl from another world who is temporarily living in our world and uses an Earthling disguise except for when she needs to transform into her true self to use her powers. In both cases, most of the occasions for which she transformed were for day-to-day events, NOT for trying to save the world. (Magical girls living solely in magical worlds, such as Kero Kero Chime or Akazukin ChaCha, do not technically fall within the genre of mahou shoujo because everyone in their world is magical; a mahou shoujo is a girl with magic powers in a generally non-magical world.) At the same time, there was a long history of live-action sentai (team fighting) series like Power Rangers. Sailor Moon was the first series ever to combine mahou shoujo with sentai: a team of magical girls trying to save the world.
The Sailor Moon manga ran in the shoujo manga magazine Nakayoshi, published by Kodansha. During its years-long run, Nakayoshi built off of that success by introducing more magical girl series, some of which were the more traditional style (Kaitou St. Tail), some which in the newly-minted team fighting style (Magic Knight Rayearth, which was also a parody of RPG video games), and one was even a parody of the genre itself which masqueraded as a typical mahou shoujo for months before introducing a plot twist (Card Captor Sakura). Most of these also met with great success. Once Sailor Moon’s run ended, Nakayoshi continued trying its luck with mahou shoujo, and met with varying success (such as Akihabara Dennougumi Pata-Pi, Cyber Idol Mink, etc.); obviously, Nakayoshi never regained thei height of popularity that Sailor Moon and Card Captor Sakura had given it.
One of the series Nakayoshi came out with in this period was Tokyo Mew Mew. It received enough popularity to get animated, and the reasons for its particular similarities to Sailor Moon are explained by the fact that it came so soon on the heels of Sailor Moon; there were very few mahou-shoujo-mixed-with-sentai series yet made for it to draw from: Sailor Moon was the main “inspiration” for it, you could say. In other words, Tokyo Mew Mew is a direct result of Sailor Moon; without the innovation of Sailor Moon, Tokyo Mew Mew would never have come into existence. Being published in the same manga magazine, the publishers couldn’t have cared less if it was just a copy of Sailor Moon churned out to turn a profit. If it did anything unique, great; if it didn’t, they wouldn’t have cared. Being from the same publisher, it didn't need to worry about copyright infringement by "stealing" any ideas. Manga magazines are growing more and more unprofitable to publish in print (evidenced by the fact that the furoku [freebies] they give away with each issue have sharply dropped in quality since the era of Sailor Moon’s run), so any hit series they can get is important. Tokyo Mew Mew did well enough, and did not need to do much original work, it just needed to utilize what made Sailor Moon and the hits of its day work. In summary, it would not occur to the creators of Tokyo Mew Mew to comment on the similarities, because that is basically atari mae (当り前, a given, obvious). Creators of ensuing mahou shoujo series from other publishers, such as Ai Tenshi Densetsu Wedding Peach or Cutey Honey F (or even the newer Pretty Cure franchise), could make comments of comparison, but it would not behoove them to do so since their series are rather obviously Sailor Moon-inspired (if not knock-offs) and Sailor Moon was dreamt up by and owned by their competition, so they wouldn't want to draw attention to that fact.
This does not actually answer the question, but here’s why I think they’re not ”that alike”:
Many mahou shoujo (magical girl) series have similar elements, especially those of same decade or genre, like both of those series are shoujo series (targeting for teenage girls or so), so finding element or two similar or same in both series is nothing strange. It’s kind of finding same kind of jokes in two different comedy series.
As plot wise, I think their plot is pretty different in nuances and narration, even if the theme is much alike. They are, after all, two series of same genre, for same audience.