If you have a business you should really have a business savings account. Although they may offer very similar features, it is better for your own internal accounting to separate the 2. Also if you have a business savings then the name on the account is your businesses name, which is definitely a better route if people are paying your business.
Specifically in terms of pros/cons of actual features, at a high level they are more or less the same.
The biggest pro in separating personal from business savings is establishing clear evidence of separateness, which is an important presumption with LLCs or other types of business entities. As a refresher, one big reason entrepreneurs form LLCs is to limit their liability to their business investment. If you have an LLC but don't open a separate business account for that entity, then it's really hard to say with a straight face that you're operating as a separate business entity.
By contrast, there really aren't many cons to establishing a separate business account. I suppose you could consider "hassle" a con, but that's likely greatly outweighed by the benefits.
As a business banker for the last 7 years with one of the largest US Banks, I can tell you that it's a matter of semantics and/or liability. There are a few ways to operate an LLC. Sole Member Managed, Multi-Member Managed, and Manager Managed. Depending on how you operate, you could use a Social Security # as a tax ID or you may need to have an EIN. The operations also have an impact on how you may file taxes. All of those are considerations in opening a business/personal savings account. If you still have questions, feel free to reach out!