(1) May and Corbyn are both absolutely awful.
(2) It's very difficult to say who is worse. I suggested, however, that May is probably worse in the long-run. (And ultimately, the long-run is the only thing that matters):
(2a) May is likely to make changes not just to our laws, but to our very society.
(2ai) Firstly, by massively restricting immigration (and quite possibly forcing out foreign citizens who are already present), she will remove many of our most reliably cosmopolitan members. Second, our population is already ageing and immigration is one of the things keeping it from going up faster - both because immigrants themselves are typically relatively young, but also because they raise the fertility of native Brits.
(2aii) Second, May is moving away from entrusting immigration control to a few sociopaths on the border and more to employers and landlords. If they employ or let to unauthorised immigrants, then they will be punished - so they will have to be vigilant to avoid this. Given the way that government enforcement tends to create public acceptance (see chapter 6), I think this is likely to further contribute to negative views of immigration and immigrants.
(2b) As Rory also notes, Corbyn is likely to fail a lot more visibly than May. Perhaps we undergo a few years of stagnation or recession, fine. Hopefully people see this isn't working and after a decade or so of self-inflicted misery, we end up with better policies. (This feels relevant, though I'm not certain how).
(3) But ultimately, this is just a guess. I would put my confidence that May is worse somewhere between 55% and 60%, and would not blame anyone for deciding that either May or Corbyn is the lesser evil.
(4) Anyone who has a reasonable knowledge and understanding of economics ought to realise that both are awful, and enthusiasm for either one indicates that you should views on politics should not, in general, be taken seriously. (This is not intended as a personal slight. There is nothing wrong with knowing nothing about politics, any more than there is with knowing nothing about car maintenance. The problem comes when one attempts to force one's uninformed views on others, rather than leaving politics well enough alone).
(4ai) Donald Trump received just under 63 million votes last year. The overwhelming majority of those were not from out-and-out racists, but rather from people who think that it is more important that the president have an R next to his or her name than that he or she be a sound thinker of calm disposition who adheres to even basic standards of ethical conduct. Party loyalty and partisanship allows people to overlook terrible flaws in their candidate; to be enthusiastic for either May or Corbyn, rather than resigned to whoever one takes to be the less bad candidate, is to place oneself in the same category as those millions who elected the ape currently occupying the White House. If the candidate one supports is less bad than Trump, this has nothing do with one's own virtues and everything to do with the fact that one is fortunate enough to live in a place with less awful candidates than the US.
(4aii) Anyone who genuinely believes in communism ought never to be allowed anywhere near government office, regardless of what they profess in order to get elected (or to be acceptable in polite society). Firstly, this belief displays a severe lack of judgement, and judgement is key to good governance. Second, the communist will attempt to implement communist policies, constrained by what they think they can get away with.
Tony Blair was acceptable is Prime Minister because he demonstrated, in particular by forcing the rewriting of Clause IV of the Labour Party constitution, that he was not any kind of communist. He was not someone who wanted communism but would settle for being able to implement liberal policies with a leftist slant; rather, he genuinely accepted the superiority of liberalism over communism. If one is the kind of leftist who ought to be entrusted with power, then one will - as a genuine liberal - be horrified at the prospect of Corbyn getting to implement his policies.
(4b) Both (4ai) and (4aii) are valid criticism of some enthusiastic Labour supporters. However, attributing both to any individual voter is perhaps to make things overdetermined. If one is a full-on socialist, then while one almost certainly despises the Tories this is hardly necessary for one to gather around the Labour flag. Similarly, becoming a loud and enthusiastic Corbynite merely to keep the Tories out has its own problems, but it does not indicate a deficit of judgement in the way that being a genuine Marxist does.