The Mongolian barbecue is terrible for veggies - it's a meat feast (I'm a veggie from Brighton who's had to cater for meat-eaters and veggies for many years - I don't know where would especially appeal to a hen party though - as a 40-something male, I'm not really qualified on that).
It depends how many people in the hen party as there aren't that many big restaurants in Brighton.
The place I love is the Lebanese place, Kambi's: great veggie meze and kebabs for the carnies - nice relaxed atmosphere too. But it's tiny (only about 20 seats, I think).
A few doors from Kambi's is a new tapas place called Pinxto People which looks a bit lively and trendy - I've not been there but I've heard good things (it's a bit pricey for tapas though). There's a great tapas place in the Lanes but 12 of you in the party will fill the place up - it's tiny.
There are the usual chains that will cater for both: Zizzi's and La Tasca are OK. There are also some good pizza places; not just Pizza Express but a few local ones: Al Dormo and Al Forno (from the same family) and Donatellos. There's also a good Chinese restaurant, Gars. in the Lanes - I've been there on a boys' night out and they coped with us.
If you want to go a bit upmarket, Due South (on the beach itself) and The Strand are excellent but you'll pay heavily for the quality.
Most big restaurants will cater for both these days - there are plenty of them down Preston Street. Now if you'd asked 30 years ago, it might have been a lot harder ....