Unfortunately, I don’t think the size of the bank has much to do with it. It’s just as likely for a large bank to give aggregators fits as it is for a small bank. As I wrote about at some length here, there’s a lot that goes into getting your data from the financial institution to your Tiller sheet. Sort of an obstacle course that your data has to successfully get through, and the obstacles are often constructed by the banks themselves.
For what it’s worth, I was just reading a long thread on another forum about frustrations with bank connection issues on one of Tiller’s competitors that uses a different aggregator than Yodlee. These issues are kind of endemic to this whole space. The only way to avoid them might be to consciously choose to put your money at institutions that have already made the switch to Open Banking standards that make data more easily accessible.