Yes, this is reasonably popular to do. It takes quite some time so it's not like people line up for it outside the shop, but I have seen several places offering this service.
I would assume that a shop in Gion should be pretty much authentic. This is finally the place you would most likely run into a genuine Maiko/Geiko. Further, the chances of getting cheated in ANY way are fairly low in Japan in general, much more so in Kyoto. From the photos both look quite genuine. You will know the difference specially on the time it takes to put on the kimono. There are not supposed to be any buttons, zippers etc on the whole thing. it's all being done with wrapping and eve very few knots.
I would assume that the likelyhood in general that someone gives you a "fake" kimono is VERY small. It's not that hard to get real ones since there are many rental companies. There are also enough services that help you wear one since it is quite difficult to do so by yourself without any help.
It might be hard however to make a judgment on the price beforehand. The cheaper places might have not as expensive kimonos and accessories. Simply the kimono can cost up to 30k USD to buy and a shop that uses nicer ones might be more expensive. Also the location is a huge factor since a house in Gion is significantly more expensive than one further outside.
I would recommend to ask the shop to send you a photo of the kimonos they have available to use for you beforehand so you can chose. They should also be able to explain what the different kimonos are meant to be for. Every season and event has different colors and patterns. It will also tell you something about the person wearing it.
Also, if you are above 170cm their choice will be limited. The amount of tall-size kimono they have will give you a picture of how many foreigners they work with.