I evaluate investments, M&A, and business partnerships for a big company.
Most of the "force them to do an NDA/MOU/make intentions clear" comments seem unlikely to work. Those comments assume that BigCo knows its intentions. Big Companies take a long time to reach decisions, so you have to give them time. Big companies have a lot of steps to reach internal consensus, and sometimes might take weeks just to get the right people in a room to make a decision, so trying to speed up their process could be like a "marry me or break-up" ultimatum too early in a relationship-- unlikely to result in what either party wants. The legitimate exception to that is if you're taking a big funding round or have external interest from another company. Overplaying that usually backfires though. The best approach is to share what you're willing to and stay engaged while limiting the amount of time the big company can take from your team. If they're taking forever to get to a decision, don't rush to have meetings: that limits your disruption while giving them more time to get to a decision. Don't hold up your roadmap unless they're committing to something or can give you a deadline of when they can commit.
Also, big companies typically won't use any NDA other than their own or sign a Memorandum of Understanding until well past the "seeing if there's room to do something together" stage.
Being too paranoid can make you seem like you're hiding something or just unpleasant to deal with and could kill a deal, but some paranoia is worthwhile. The key is being paranoid about the right things.
You should obviously talk to a lawyer to understand the protection the existing NDA gives you, but there's really no purpose in getting a stronger NDA until they've made up their mind what they're doing (because until then, they won't sign one anyway). Unless you've come up with something dramatically new in your architecture (as in you don't use Map-Reduce because you invented something much better), sharing the architecture can be a good way of building some trust and helping them understand how they might integrate without giving too much away. I don't see a big company doing things like changing their architecture or algorithms because they found a better way to do things-- there's just too much inertia to changing those fundamental things in a product if they're close to market, and they'll be sensitive to IP issues too. You should be more worried about them learning from your knowledge about effective customer/selling tactics or about them sizing you out as competition (which would focus on features instead of technology). You usually wouldn't protect yourself against that much in an NDA, so you need to be smart about sharing enough to impress them without giving them too much.
It's usually a bad idea to let them look at code at all until they have an agreement in place about their intentions (that's when the LOI or MOU comes in). They should be making a big effort to protect their own people from IP pollution at that point. If they're wanting to look at code and don't have formal agreements in place, you should wonder if you're really dealing with the corporate part of the company or just some random product team that isn't going through the process they should (which could innocently be because they don't know what process they should be following).
One good way to judge how serious they are is who you're dealing with. If you're just dealing with engineers or junior PMs, it isn't serious at all. If there are more than 2 levels of PMs involved, then they're probably really considering doing something.
Similarly, you can try to tell what direction they're leaning for the relationship. If the titles of the people leading the discussions are Business Development or Solutions, they're probably leaning towards a commercial arrangement, if there's Corporate Strategy or Corporate Development involved, they might be looking at M&A. Don't draw conclusions about the likelihood of M&A from the Corp Strategy or Corp Dev titles though-- it only tells you that's the direction they're looking at it, not how serious they are.
Rather than trying to force an agreement, you can test how much visibility the effort has by trying to get a meeting with a senior executive (someone who runs a product area or BU) and see if they make it happen.