I played Harvest Moon DS and DS Cute and I loved both of them! I've played sooooo many Harvest Moon games in my life and the whole series is awesome.
If you're looking for games more like HM DS,
A Wonderful Life for the GameCube takes place in Forget-Me-Not Valley as well, since HM DS is kind of based off that game. Out of all the Harvest Moon games I've played, A Wonderful Life is easily in my top 3 favorites. The game is visually beautiful, the characters have pretty good dialog that actually changes with weather and seasons, and I feel like the game is pretty simple and easy to enjoy. The only problem with AWL that I have is that the game can come to an end. Meaning, you can't play for like 100 in-game years. I don't want to spoil anything incase you get the game, but keep that in mind.
Another HM game more similar to DS is
Friends of Mineral Town for GBA and now on the WiiU Virtual Console. Friends of Mineral Town takes place in Mineral Town (obvs) and if you had the GBA cartridge, you could put it in the DS, when they still had GBA slots, and unlock Mineral Town potential bachelorettes in the HM DS game! If you look up gameplay of Friends of Mineral Town, you'll see how extremely similar the game looks to HM DS.
Friends of Mineral Town is also in my top 3 Harvest Moon games. The town is great, the characters aren't as great with dialog like with AWL, but the mechanics are simple and I find the game extremely fun. Farming and taking care of animals isn't very difficult and the festivals are pretty fun!
I think my 4th favorite Harvest Moon game of all time is
Animal Parade for the Wii. I just got it not even a year ago, but the game quickly became one of my favorites. The farming is easy, the town is nice and the scenery is pretty, the bachelors are super cute (bachelorettes are as well), and there's tons of animals you can have. One of the coolest things I haven't even gotten to experience in the game yet is that you can have more than one child in your family! I thought that was a really cool addition and I'm still working my way towards getting that

this game really isn't anything like Harvest Moon DS, none of the characters are the same nor is the town, but I really think it's an honorable mention if you want to really play a game that's true to the Harvest Moon name.
I found that Harvest Moon DS was a really great addition to the Harvest Moon name, along with games like A Wonderful Life and Friends of Mineral Town. But I really didn't find the game A New Beginning to be a very good representation of what Harvest Moon games are really like and I feel like it's not even close to what kind of HM game DS was. The game is pretty watered down, imo, and I got bored of it really quickly. I just wanted to give my opinion on this game if you were considering it.
And as for Story of Seasons, I never played it because I was pretty sure it was going to be just like A New Beginning, and I didn't really want to be disappointed again.
Ugh I keep forgetting stuff lol
If you want to look up information on certain games,
www.fogu.com is a great site for all your Harvest Moon information needs!