I think there are different answers for different cases. For example, if you and that established company are in a rare business, your position might be a diamond to them. Of course if you're good at what you're doing.
Because those companies already have an end user characteristics. It's hard to break that and they probably can't change things the way they would. That gives you the advantage of being free. You can approach the same problem from different angles and apply solutions more suitable. If you're good at what you're doing, they'd prefer to get you in instead of going against you.
On the other hand, those "established" companies have an advantage in the market for complex businesses which require different assets at the same time such as technology (software and/or hardware), delivery, service, etc.
A bank or any other large scale finance company would be a good example to that case. Because they are already in the market and they have their licenses to do business in various areas. They have their payment devices (POS, ATM, Mobile App, etc. any kind of device.) They have call centers, lawyers and most importantly they have customers.
With all these information, let's say you want to build a new payment or money transfer method which they already kind-of-have but you're sure that you can make it better. In that case, being a new product in the market without any partnership with an actual finance company would be painful.
I think the key here is that to focus what we can do on our own best at the beginning. That approach would keep our product as simple as possible. If it goes well and get some attention, then we can think of what to do next with our competitive product.