I have limited experience in terms of relationships (as in, not a large sample size) so I'm not really sure how much weight my words gives here. But I'll answer as well as I can.

I think it's easier for women to get sex atm just looking at our culture and how people generally behave. If a guy goes up asking random girls for sex he's usually called a pig and avoided. If a woman goes up asking random guys for sex, most of them will say yes without hesitation.

As for relationships? I'd have to also say women, mainly for two reasons.

1) As highlighted above, most guys jump at the chance of sex. Many may also agree to a relationship in the hopes of sex.

2) Culturally, men are expected to pull most of the weight and 'be the man' in terms of asking a girl out, providing a good date etc.
Unless if there's a specific guy the girl want's who isn't bothering to ask her, getting into a relationship for a girl is basically as easy as waiting for a boy to make a move.
If you're a guy, there's a chance the girl will make the first move (Like both my mine ended up getting started), but it's not going to happen as often.

Is it easier to get a romantic relationship or friends with benefits?
I don't think there's a clear answer here, this largely depends on the area you live in and the people you interact with.
You could be around mostly people who save sex for people they love, or mostly around people just treat sex as a pleasure thing.

As for which is easier to maintain? I'd say friend's with benefits.
Relationships require a lot of time invested in the other person, to be supporting one another, emotionally available, etc.
Friends with benefits, all you really need to do is have both people wanting sex and you're good. 
Granted friends with benefit's can be more complex than that, but it doesn't need to be complex at all in order to count as friends with benefits.