Some antimicrobial compounds will work on both G+ and G- whereas others will only work on one or the other. In fact some are even more restrictive and only work on certain G+ or certain G-. You could still call them antimicrobial compounds but with restricted target population.
It probably depends on the application you need it for. How do you plan on using this antimicrobial? What are the bacteria that will likely be found in the environment of use?
There are some substances that work against both Grame positive and gram-negative bacteria such as broad-spectrum antibiotics works against both, but there is difference between the cell wall of both.
It is important to note that a substance is termed antimicrobial if it is active against a range of microbes (say bacteria and fungi). However if a substance is active against bacteria is termed a bacterial and antifungal when active against fungi. Now to your question, a substance can be antibacterial if it is active against either Gram positive or Gram negative irrespective of the type of bacteria based on the cell wall composition. Additionally, if a substance is active against both Gram positive and Gram negative bacteria, it said to be a broad spectrum antibacterial substance. Wishing you all the best