Actually, based on the dimensions and resolutions you provided, the two files have exactly the same number of pixels. Multiply 27" by 72 ppi and you get 1944. Multiply 6.something by 300ppi and you get the same (1941, if I remember--rounding error in the math).
PPI is most useful when you're printing (oversimplification), otherwise you can mostly ignore it. The real question is why the tiff looks blockier than the jpeg, when it sounds like they have the same pixel dimensions. I'm puzzled.
In general, the primary advantage to RAW is the ability to alter the whitebalance easily, and also to change the exposure without losing any data. It's a nice perk that the image doesn't have lossy compression like a jpeg, but again, in general, you don't get a practical benefit out of that.
All of which is to say, jpeg isn't a bad thing at all while you're still practicing.
But you should be able to do what you're interested in, in RAW, so don't let this drop if you're really interested in it.