If Bi-Wiring is an option, should I choose Bi-wiring over single banana with free jumpers

My issue with the jumpers shown in your picture is that it would be very easy to create a short circuit and damage your amp or speakers. To bi-wire or not to bi-wire is a bigger discussion. Simplest would be some high-quality jumpers, As stated many times above.  I’ve had success with WBC, “world‘s best cables”, reasonable cost, quality bits, solid build.

My plinius sa 100 has four binding post each side , my diapason adamantes has also 4 binding post. When I used 4 single run cable each side . I get huge soundstage and good layering, effortless sound.Lak is right 2 and 3 fast answers on cabling you have to experiment, to get the sound preference you like.

@steve_a001 Kimber-Kable 12TC speaker cable, 8ft long, has 0.006 Ohm resistance and less than 1uH loop inductance, which makes interconnect between amp to speakers terminals “invisible”. If cable is too long (high R and L), then there will be some improvements of bi-wiring.

Jumper/SPKR-terminals/SPKR-internal-wiring-crossover quality can be very bad quality, many folks will be surprised to see 0.5Ohm LPF (bass) SPKR inductor resistance, and very tiny wires inside SPKR cabinet.

The simple answer is yes, bi-wire. My experience is that bi-wiring always improves all areas of sound quality.   The reasons are listed.  

1. First, if you do not bi-wire, and your speakers came with unshielded metal jumpers (like my ‘97 vintage Apogees) or poor quality shielded wire jumpers, then replace them with wire equal to, or better than, your speaker cable.  Electromagnetic interference, including radio frequency interference, will enter a circuit at the weakest shielded point.  So it is important to have a quality jumper.  Also, you want a quality conductor to not limit current flow by increasing resistance.  My Apogee speakers sounded harsh, grainy, and with polite bass using the OEM jumper.  
2. Second, low frequency drivers demand more current than mid/high frequency drivers.  As current flows through a wire, electromagnetic force develops.  EMF creates high frequency distortion.  By separating the current demand, less EMF is developed in the wire for the mid/high frequency drivers.  Therefore, theoretically better SQ.  
3. Third, bi-wiring obviously increases the amount of conducting material reducing gage.  Doubling the wire is not directly proportional to gage number, so the total will not half.  But it will go down a couple of units.  Decreasing gage reduces resistance and permits easier electron flow, thereby improving sound quality.  
4. Bi-amping is the ultimate form of bi-wiring.  I never had a budget to bi-amp.  The technology discussed above applies.  In addition, you benefit from two power amplifiers, each with the own power supplies, one handling current demands of the low frequency drivers, the other handling the current demands of the mid/high drivers. 
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In conclusion, bi-wiring technologically makes sense.  My experience has been it improves all areas of SQ with my speakers in my system.  My recommendation is to get a demonstration pair of bi-wire cables of your choice and determine if you get improved SQ and if the benefit/cost ratio is worth it   

"unshielded metal jumpers” - curious, how do you shield jumpers?