Chelsea announced on 21 September that they had agreed to a deal to sell Costa back to Atletico Madrid, subject to the agreement of personal terms and a medical.
The 28-year-old scored 20 league goals to help Chelsea win the Premier League title, but his relationship with Antonio Conte broke down in the summer after the Blues boss informed him that the striker was no longer part of his plans.
Chelsea signed Morata for £60m ($81m) from Real Madrid, and the Spaniard has been entrusted with spearheading the Blues' attack in the absence of his Atletico-bound compatriot.
"I would rather have Costa than Morata in my team at this moment in time, to be honest with you," Neville told Sky Sports.
"I think he is better suited to the English game – Morata has great potential, but if you were an opposition manager, you would rather be facing Morata than Costa.
"[Costa] is a fantastic player, he scored goals and is someone you would think, 'I'd love him in my team'," the former United and Everton defender added.
"Morata is different, he thrives off crosses. Costa you can stick him up there on his own, he will take on the whole of the back four, from the left back to the right back to the centre back. He will try and bully them all.
"Whereas Morata is a little bit more cute in his movements, he thrives a little bit more on crosses, he keeps it pretty simple outside the box."
Morata has scored three goals in five league appearances for Chelsea this season.
The Blues' next league assignment sees them taking on Stoke City at the bet365 Stadium on 23 September.