The Wales international's representative believes the 24-year-old has more ability than the Brazilian and admits the deal to bring the midfielder to Spain was "problematic"
The Wales international secured his £86 million move to the Spanish club from Tottenham in the summer transfer window, while Barcelona bolstered their attacking options with the acquisition of the 21-year-old Brazilian.
Neymar scored his first La Liga goal on Tuesday evening but Bale's representative believes the 24-year-old is ahead in terms of ability.
"Bale has played in the Premier League and has won a lot of trophies. For me, he's better than Neymar," Barnett told La Sexta.
Barnett also admits the deal to bring Bale to the Santiago Bernabeu was "tough and problematic", while Goal revealed earlier in September that Manchester United had launched a £125 million bid for the 24-year-old.
"The deal never fell apart in the end but it came close on several occasions," Barnett said.
"It wasn't all peace and love in the meetings. Negotiations were tough and problematic.
"Tottenham made us a great offer to stay and there was another club that offered much more than Real Madrid."