Note: I've only played the original Harvest Moon on the SNES and Rune Factory 2, so my opinions are based off playing those two games.
Rune Factory 3 (or as it feels like, 2.5) starts the same way the other Rune Factories start: Man with amnesia wanders into a town and is given a farm to look after by stranger. You can then grow crops, befriend people and monsters, and explore the seasonal dungeons that surround the small town. Through completing the dungeons and requests of townsfolk, you slowly begin to regain your memories and remember the reason why you came to this place.
There are a few improvements from the gameplay of Rune Factory 2, the main ones for me being:
*The ability to take townsfolk with you into dungeons, allowing you to equip them with weapons and accessories, and magic seeds that provide a variety of uses (transforming into weapons, modes of transportation, etc).
*Deeper crafting system: You can now fuse effects and resistances onto weapons and accessories (instead of just increasing their base stats), giving them the ability to paralyze, stop them from casting magic, and even steal HP from enemies.
*Deeper combat system: More weapon types and moves that unlock the higher your skill is in that weapon type. Also more intelligent monsters make bosses and mobs a little harder then previous games.
*Better frame rate: When too much happened on the screen in RS2, it would get pretty choppy. RS3 is in general much smoother and only chops up a bit when nearly everything on the screen is moving.
*Combat stats improve from farming: Your skills such as mining, farming, logging and fishing now increase your HP, RP, Str, Int, ect, allowing you to improve you combat capabilities while doing your everyday activities. Hilarious skills such as walking, eating and sleeping now exist too, so simply sleeping at the end of the day will improve your statistics.
However, there are a few criticisms:
*Story is not as good: After how good the story of RS2 was (and from what I have heard, of RS1), I was hoping it would only get better from here, however it was disappointing.
*Lots of fetching items: This isn't as bad as most items (bar flowers and crops) are fairly easy to come by, however nothing is frustrating as someone asking for a flower that take 15 days to grow, for example, which leads to...
*Growing anything in Summer and Winter was DS ripping level of frustration: Hurricanes and blizzards happen in every Harvest Moon/Rune Factory, however it seemed to happen a lot more often to me in RS3. I don't know if it was me being unlucky or not, but spending twenty thousand coins on crops only to have 90% of them destroyed in a few days is just annoying. Which also leads to...
*Almost no reason to ever grow crops or craft items: They released a dungeon underneath your house that can also be done co-op, however the issue is that the drops from this dungeon are simply too good. Not only are there rare crops and seeds that are dropped from monsters/chests, but also the best weapons and accessories in the game are found here. For instance: The axe I use I found here requires 83 forging to create, and even focusing on forging, I still only ever got it to 50 by the time I finished the game, and I also found an Art of Magic which requires high 90's crafting to make (level 100 is the skill cap), a skill I only got into the mid 20's. A side effect is that because these items are so good, you can sell them for thousands of coins, I had made 400000 after spending two game weeks in that dungeon making farming for money a non-issue. Pharmacy and Cooking are the only craft skills worth leveling.
*Nearly every sprite is the same from RS2: This is just a nit-pick, since even though I loved the old sprites, it would of been nice if they got a little bit of a makeover.
*Simply too short: I want to play more of you Rune Factory! After the main story is complete you can continue to play, however for me that's when I put a game down. There are a bunch of trophy's you can unlock (such as playing for 5 in game years and collecting 10,000,000 coins) if that's your thing, and the dungeon under your house requires you to be a very high level to complete.
Despite these criticisms, It is still a fantastic game that I played at every opportunity I had until it was done. The characters draw you in and you want to know what happens next. Since the games are simply set in the same world and are not linked, you can pick up RS3 without playing RS 1 or 2, however if you are completely new to the series, you should play Rune Factory 2 first as imo it is an overall better game.
Rating: Buy it.