I can only share what I've learned (the hard way), as I'm in the process of working on a product that is applicable to both large and small as well.
The first thing I would ask is, have you validated your assumptions of its applicability to both by asking potential customers from each?
If so, are there fundamental features/functionality that you can distill out and put into your product that both would use?
I went into interviews with customers (small and large) with assumptions that needed to be tweaked ultimately based on the resources available to each. In other words, larger organizations may have more money, but not the flexibility (sometimes) to buy/use your product whereas small businesses don't necessarily have time/money to spare, or the technical aptitude, but are more flexible to having their problems solved. Taking those items into consideration I was able to come out with something that appealed to both.
From there I turned to marketing. As a single founder (for now), I was driving myself insane trying to figure out how I would market to both groups, slicing and dicing all sorts of information. It wasn't beneficial and I finally had to draw a line and go after small groups to start. This provided to be better, quicker wins...you are typically dealing directly with the decision maker. And I can turn easily these folks into advocates for my product by providing exceptional customer service. Something that may be hard to do with a bigger organization.
Once I have traction here, and additional resources I plan to go after larger organizations.
Its easy to get excited at the thought of tackling both at once, but along the way focus will be lost somewhere. It really comes down to the resources you have available and where you think you can gain the quickest traction. From there, you can then work on scaling.
Hope this helps. All the best.