Yes, the AVB's better results against Norwich, Chelsea and Hull had home advantage. Likewise TS's better result against Everton had home advantage.
The two results where TS did substantially better were the wins at Saudi Sportswashing Machine and Man United after a home loss and draw, respectively, so overall he did do slightly better. He deserves credit for bring bringing back Adebayor and giving some young players a chance.
The question has to be did he do sufficiently better to deserve the full-time job, as let's face it, we all know he was caretaker manager in all but name? Did we see signs that there would be a significant improvement long-term or can most of the difference be attributed to their different handling of Adebayor?