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I am designing a measuring instrument powered by a Li ion Cell, I need to display remaining battery capacity on it, so I was wondering what is good or lets say widely used method.

Should I use full fledged Battery fuel gauge IC instead of just measuring battery voltage to display remaining battery.

My second question is, since current draw of my instrument would be fairly constant throughout the run, so is it possible to estimate capacity from Battery voltage and current draw?

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It's possible to get a very rough estimate for battery capacity from voltage and current draw, but as the battery ages and as the temperature changes it will lead to very significant errors. Probably the best method out there is impedance tracking, which you can read about here:

http://www.ti.com/lit/an/slua450/slua450.pdf

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