eof() checks the eofbit in the stream state.
On each read operation, if the position is at the end of stream and more data has to be read, eofbit is set to true. Therefore you're going to get an extra character before you get eofbit=1.
The correct way is to check whether the eof was reached (or, whether the read operation succeeded) after the reading operation. This is what your second version does - you do a read operation, and then use the resulting stream object reference (which >> returns) as a boolean value, which results in check for fail().