I have about as much faith in Corbyn to get a good deal out of the EU as I have in May to do so, which is none. They would approach it differently, but the EU is in a far better position than the UK and who the UK PM is won't change that in the slightest. There's no reason for the EU to give the UK a sweetheart deal and plenty of reason for it to not do so. Right now, the officially UK position is that it shouldn't pay money it's already agreed to pay and that the EU will cheerfully go against its own interests to favour the UK. Why would it do that? The main thing the UK has is banking, which could be done in Paris or Frankfurt or half a dozen other places in the EU. If the UK does a hard brexit, especially one without any kind of deal, why would transnational banking interests stay in the UK rather than move to the EU (i.e. a much bigger and much more international market)? Especially when the EU offers the banks a sweetheart deal, which it should do because that would be in its own interests. Then there's the smaller but still very significant matter of foreign business interests in the UK. Why keep them there when there's a much bigger market nearby? Of course they wouldn't immediately shut down and eat the loss that would result, but it would be in their own interests to transition to the EU over time. The UK can't even feed itself, let alone sustain its own economy against a much bigger market. We need deals with other places and the EU is the most important by far because of its size and proximity. The EU doesn't need the UK. You can't get a good deal with a bad hand regardless of how bull-headed you are and regardless of how many people think that's what strength is.
When it comes to internal government, I'd rather have a person picked at random off the street than May. Even if that person is a baby too young to even speak yet. I'd rather have Siri than May. I'd rather have an empty chair than May. China and North Korea are taking lessons in internal government from the UK now. That's how authoritarian May is and how skilled in propaganda. I think Corbyn would be rubbish at the job, but I think he'd do less harm.
Right now, I'd rather have the Queen act in her own name with her own authority than either of those two being PM acting with her authority. Queen Elizabeth II is a much better ruler than Queen Theresa I. But I'd rather have a liberal (real liberal, classical liberal, not the grossly illiberal modern corruption of liberalism that's spewed out from the USA to infect here too) PM acting with the strength of consensus and co-operation.
Corbyn would do just as much damage just in a different way - a lot of international business and the financial industry have a significant presence or are HQ'd here precisely because we are one of the most stable and secure countries in the world and Corbyn would undo a lot of that.