Women are at a serious disadvantage regarding romantic relationships since time is less kind to them and it becomes difficult to ignore your biological clock when it starts blasting louder than a Monster Magnet concert. Then (and I think this is also hugely important) you have to deal with all the ugly shit that lands onto most people when you are in your 30's. Job, family and daily duties tend to suck the vitality of most folks by that age and change their personality towards stability, nullifying our more adventurous tendencies. This is just time doing its thing.
Your 30's are also an incredibly complicated time of your life. Most people are married by that time and probably even have one or several kids. Single and thirthysomething usually means that you are either divorced or had late a break-up. Both situations can mess you up pretty badly. The baggage is real. People require some time to adjust at an age bracket where most women start feeling like they can't stay put due to biological and societal pressures. If they want to have children (and there's absolutely nothing wrong with that) they need to act with some diligence. Things can get even more troublesome for women if there are already kids involved, since many single men want none of that (let alone dealing with ex-husbands if we are talking about divorced persons) and women also happen to be the primary caregivers of young children, drastically reducing their spare time.
Then there's physical attractiveness. I personally know quite a few women in their 30's who easily outrank 99% of any potential competitors in their 20's, but there's no denying the female body requires some important maintenance that the male body doesn't due to hormonal and body composition differences. Your 30's are a bitch, too. Fat gets stored differently and the body becomes less firm. Significant exercising and a proper diet (at a time that is probably the most stressful of our lives) is a must if you want to stay competitively attractive. For every rep you do at the gym, she probably has to make two. Factors such as sunlight and excessive smoking compound, too, doing a real number on the face. And then you have all kinds of films, TV shows and magazines reinforcing the image of older men being more attractive/younger women falling for them. Which is an awesome boon for us, but not really fair for women past their 20's. I mean, my partner is considerably younger than me, but I still find the age disparity in Hollywood movie couples just plainly absurd.
With that said, most of what I said applies to building a relationship. If you just want a date, it doesn't matter if you are a man or a woman: your 30's will probably the best time of your life. You have some actual income, probably a place of your own and/or a car and life experience, which is the biggest draw there is. There are also a lot less taboos and fears regarding casual sex. For all the Millennial moral outrage in the press, nobody has it easier than single thirthysomethings on the prowl. Nobody.
I basically wasted most of 20's since I made my career my only priority. Dating during my early 30's was a revelation. I only wanted to meet women of my age at first since I thought those would be the ones I would find the most relatable, but a huge amount of them wanted to meet their life partner first and foremost. Children were also a huge concern. I lost the count of the times somebody would bring kids to the conversation as soon as during our second date, which was a complete turn off. I met some amazing single women during that time, but as someone without any particular romantic aims, the amount of incompatible partners in their 30's became troublesome, if not borderline concerning. So I decided to expand the age bracket, only to find that not only it was extremely easy for a man in his 30's to date girls 10 years their junior, but also that younger women had less expectations and a more carefree attitude that made dating much less stressful. Being able to date someone without the pressure of knowing that she had given herself a defined window to asses your quality as a person before deciding if you were "the one" was a huge relief. From that moment I found myself dating mostly younger women; not because that was my strict desire, but because things played out better that way.
As far as my experience goes, technically speaking women in their 30's have little issues dating men of their age and older. As a matter of fact, they have it easier than ever. But getting a date and building a relationship are massively different things, as many single men in their 30's don't have the same aims nor share the same pressures that women do. Biology and society allow men to extend their 20's for a good couple of decades, whereas women are not that lucky.
