Hi, as of the last time I went flat-hunting (early this year)...
The partially furnished places we looked at had "white goods" - refrigerator, airconditioners, washing machine, stove, and sometimes a dryer.
The fully furnished places had what the P/F places had, plus usually a microwave, TV, dining table, wardrobes (sometimes built in, sometimes free-standing), a living room set, and beds with mattresses.
Haven't had much of a chance to compare rentals between PF and FF places, as the furniture wasn't really a deciding factor for us (we have some of our own stuff). You can usually negotiate to with the landlord to add one or two appliances or a free-standing wardrobe for you, for free.
If the landlord wants to charge for the additions though, things are pretty cheap here at Ikea and in appliance stores, so it may be cheaper to buy the extra things you need on your own (and you'll get to choose your own style).
If you are looking for a 1-2 BR place, you will likely be better off not bringing your furniture from India. Many 1-2 BR flats are rented furnished, and if you have your own stuff (like we did) you may have a problem if the landlord doesn't have the extra storage space to pull out what's already in the unit.
Having a lot of your own stuff will make it complicated when you need to move to your next apartment... say, when your lease expires. We learned this the hard way!
So you are on the right track, just bring what is necessary. You might find that you may not even need to buy a lot of stuff here in Singapore, if the flat you rent already has what you need.
