I feel the opposite way; I think
Diane sounds more modern and
Diana sounds more classical. I guess that there is a trend for -a endings, but there is one for -e endings too:
Madeleine,
Charlotte,
Natalie.
Sophia and
Amelia are both popular, but so are
Sophie and
Amelie.
Caroline's more popular than
Carolina;
Melanie's more popular than
Melania. Still, though, I get what you're saying. But I feel like
Diana's unpopularity will cancel out the trendiness of the -a ending.
Diana is, in itself, untrendy.
I sure do prefer
Eve over
Eva, though. But mostly I prefer the -a endings:
Anna,
Julia,
Eliza (over
Elise),
Louisa.