Need help on-parallel resonant circuit vs. bandpass filter!
You have a misconception. Just like you try to compare "when should I use a wheel and when a vehicle - what advantages and disadvantages they have over each other?"

Offtopic: the difference may sometime have been quite small

http://images.tcj.com/2012/03/Hart-9-650x937.jpg

A parallel resonant circuit can be a part of a bandpass filter. Bandpass filters can be realized with or without resonant circuits just like vehicles can havve wheels, but for example a hovercraft doesn't.

Parallel resonant circuit added to be in parallel with a load and feeded from a signal source with non-zero internal impedance was the simplest form of bandpass filtering that was selective enough for separating different radio stations. That historical fact has made it important and was a reason for serious theoretical and empirical investigations on how the basic circuit should be built and how the circuit can be developed for better performance.

Today we have the circuit theory and we can calculate or look up the tables to find, if 2nd order bandpass filter is enough for a filtering purpose. If the answer is yes, then a resonant circuit can be ok choice. A single resonant circuit fulter definitely is not enough, if steep passband slopes are needed and the wanted bandwidth is not small when compared to the passband middle frequency.

Most practical limitations of the LC resonant circuits are caused by the non-ideal coils. They can be too bulky, have too much resistance  or the needed coil is too small to be mostly a coil, not a complex composition of capacitance, inductance, resistance and working as an antenna.