No - It is not a question of consistency, the same model is used in both cases. Any difference in score (given the same CRA) is data in the CRA report at the time it is input into the scoring model. Generally the more recent the data has been pulled to generate a score, the more likely it is to represent current state.
As for scores being accurate - if the data in your CRA report is accurate your score will be accurate. Otherwise garbage in, garbage out.
Fico 9: .......EQ 850 TU 850 EX 850
Fico 8: .......EQ 850 TU 850 EX 850
Fico 4 .....:. EQ 809 TU 823 EX 830 EX Fico 98: 842
Fico 8 BC:. EQ 892 TU 900 EX 900
Fico 8 AU:. EQ 887 TU 897 EX 899
Fico 4 BC:. EQ 826 TU 858, EX Fico 98 BC: 870
Fico 4 AU:. EQ 831 TU 872, EX Fico 98 AU: 861
VS 3.0:...... EQ 835 TU 835 EX 835
CBIS: ........EQ LN Auto 940 EQ LN Home 870 TU Auto 902 TU Home 950
