A small addition of 2 mole% fraction of ytteria to scandia stabilized zirconia results in the formation of cubic phase where two phases-tetragonal/ cubic can coexist. The presence of cubic zirconia lowers the actvation energy[0.65eV from 0.95eV] and would allow the electrical conduction easier.

{PLS LOOK IN THE SECOND PARA ON PAGE-942 of Electrochemical Society Proceedings Volume 2005-2007.pp-940- 946 : Attached along with; Zoom150-200}

The tetragonal modification undergoes a catastropic transformation under hydrothermal conditions at 300C and precipitates in the presence of water which is formed during the operation of the  cell which reduces the conductivity.In fact , the degradation and the failure of the fuel cell is due to the presence of tetragonal form.

I don't work on SOFCs but a quick google search and I found this paper:

M. Mori et al. ~Solid State lonics 74 (1994) 157-164

It has 121 references according to google scholar and seems reputable. In it, they say:

"8 mol% yttria stabilized zirconia (8YSZ) has been extensively used as an electrolyte in SOFC because of its low electronic and lfigh oxide ion conductivity, as well as excellent chemical stability under reduced and oxidized atmospheres at a high temperature. However, to obtain the high performance planar SOFC, especially the electrolyte self-supported planar configuration, the YSZ electrolyte should meet the following requirements adding to them the above: ( 1 ) high fracture strength and toughness; (2) excellent thermal conductivity; (3) good compatibility of thermal expansion with the other cell components 

Yttria-stabilized tetragonal zirconia (Y-TZP) with 3 mol% Y203 has a high bending strength at room temperature (RT) [ 2 ], and the electrical conductivity was found to be 6.5 X 10- 2 S/cm at 1000*C [ 2,3 ]. The strength of Y-TZP, however, decreased remarkably with increasing temperature. The addition of Al203 improved the high temperature strength of pure Y-TZP, because the strength of alumina does not decrease as much as that of zirconia with increasing temperature [4] although the conductivity decreased with increasing Al203 content. The electrical conductivity of 3Y-TZP with 20 wt% Al203 was 4.5 X 10 -2 S/cm at 1000*C and its conductivity value is slightly lower than acceptable as the electrolyte in SOFC with high performance [ 5 ]. Many papers have been reported on the effect of small Al203 addition to YSZ on the microstructure and the resistance. A small amount of Al203 addition was effective for densification of YSZ [6,7 ]. Few papers have been published on the mechanical and electrical properties of the YSZ and Al203 composites [ 8,9 ]. By adding about 20 wt% AI2O3 to YSZ, the mechanical strength was increased by 50% [9 ], and the electrical conductivity was decreased by 25% [ 8]. The YSZ- AI2O3 composites are quite attractive for the electrolyte in the planar type SOFC. "

So it seems the answer is yes, the cubic phase has better transport properties. However, that is possibly too narrow of a view since the mechanical properties may not be sufficient at the operating temperature. 

If you need to be familiar with zirconia, I would recommend you to go through the basic literature on the subject. Solid Electrolytes and Their Applications by E. Subbarao (Editor) and the series Science and Technology of Zirconia are good options.

Your question is not as simple as it might look like. That relationship has been addressed for more than 50 years now. Under the following link you will find my dissertation, which contains a decent literature survey about the relationship between structure and electrical properties of YSZ (until 2010, of course not complete): http://digbib.ubka.uni-karlsruhe.de/volltexte/1000015724

For the tenary system Y2O3-ZrO2 even 8.5 mol% of yttria is not sufficient to stabilize the material. Here are some of our recent studies dealing with the decomposition of 8YSZ and the enhancement of the decomposition rate in the case of Ni is dissolved in the 8YSZ, e.g., incorporated from the anode side:

- Decomposition of 8YSZ: http://www.sciencedirect.com/science/article/pii/S1359645409004790

- Accelerated decomposition of Ni-containing 8YSZ: http://www.sciencedirect.com/science/article/pii/S0167273812000926

You will also find some full-text versions of the above-mentioned manuscripts under my account.

“Does the cubic phase have high ionic conductivity compared to the tetragonal and monoclinic phases?” Yes, definitely. Cubic phase has high ionic conductivity than other phases because it has equal oxygen vacancy site in all directions through whole lattice structure.