Differences between HM64 and Back to Nature: This should cover the basics.
Gameplay:
-Rucksack. In Harvest Moon 64, you have to go into the menu to pull tools and stuff out. In Back to Nature, there is a button that will let you cycle through stuff.
-Basket. In Harvest Moon 64, you are limited to your rucksack. In Back to Nature, you can buy a basket that can hold 30 things (you must ship them however)
-Festivals. HM64 has the Egg Hunt, while BTN does not. BTN however has a swimming contest, a chicken sumo contest, and a tomato festival (where you must throw tomatoes at the other team)
-Tool upgrades. HM64 has tools upgrade automatically. In Back to Nature you must mine for minerals, and pay to upgrade them once you have used them enough.
-Marriage. Cosmetic difference mostly, in 64, you have 5 heart levels. In BTN you have 7.
-Farm Size. In HM64 you have a medium sized farm. In BTN you have a large one.
-Horse. In Back to Nature, if your horse doesn't like you enough, it can be taken away.
-Crops. HM64 has a small selection of crops (around 3 per season) while BTN has a larger variety (4+ per sesaon)
-Bees. In HM64, there are no bees. In BTN you can get bees to come to you. You can harvest honey once per day.
-Cooking. In HM64 recipes are for collection purposes. In Back To Nature, you can actually cook the recipes. You have to buy utensils however.
-Town Layout.
In Harvest Moon 64, the town layout is pretty simple. There aren't a lot of turns you can make. Your farm is VERY simple.
In Back to Nature, the town layout is more complicated. It's not hard to learn, but you DO have to explore a little. Your farm is a little more complex, with more than one entrance.
There are also character differences, but it's probably best to discover them for yourself.
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See You In Another Life, Brother.