I've only played the very first rune factory and that was quite a while ago so I honestly can't give you too much information on them...
On harvest moon though, I can tell you this about story....there really isn't one. Yeah pretty much that. I mean there is a LITTLE story...your grandfather gave you a farm to fix up or you have to help find all the three animals to get them back to the parade or you have to win cooking festivals to reunite the two towns...
And that's about it. It's left pretty free and open so that you can live your life how you want and you don't have a big overarching plot to deal with while your trying to get the hottest bacholer/ette in town to finally fucking take the damn blue feather!
As far as Rune Factory goes, from what I can remember of it, there was quite a bit more plot invovled, seeing as you had caves to explore and monsters to defeat, but you also had the essentials of Harvest Moon, taking care of a farm and finding your sweetheart...maybe even having a kid but like I said this was YEARS ago so I could be wrong. But, if memory serves, I found it a little difficult to try and do all this cave exploring when I was also having to tend to a farm and only had so much energy in the day.
Also you might look into Innocent Life. It's kind of a futuristic Harvest Moon, you can't get married in it, but you have to tend to a farm and it has a much more overarching plot involving restoring nature or some such and involves some exploration, without having to go off and kill monsters.
Anyways, it all depends on what appeals to you, I would go to amazon and just type in Harvest Moon, Rune Factory, and Innocent Life and just compare and contrast the results you get and see what appeals to you. Something you might be intersted to know is the newest Harvest Moon, A New Beginning, came out last November and has some new interesting points in that you can now design your character's looks AND design the layout of your farm and possibly your home as well.