In short, yes. The resolution of your content - be it in a landscape or portrait orientation, High-Definition (HD), Full High-Definition (FHD), Ultra High-Definition (UHD), or something else entirely - can have a significant impact on the performance of your digital signage device. The reason for this is down to two key factors: the processing power of the signage device you are using, and the screen on which the content is being displayed.
When focusing on the screen itself, it's important to understand the native resolution. It's always prudent to publish content to your screen that matches its native resolution. This means the player does not have to work harder to render the content to fit the screen. For example, a player may struggle to down-size content that is UHD to fit a screen that is only capable of showing FHD content.
It's also important to consider resolution if you are publishing content in a layout zone. Inevitably the resolution of a zone will be lower than the screen itself, so content might have to be encoded to fit said zone in order to get the optimum performance out of your signage device. This is where the processing power of your device may come in to play, and whether it is capable of handling this without encoding your content.
Below outlines the more common resolution sets today (landscape):
High-Definition (HD) : 1280 x 720 pixels (less common now as would be considered relatively low resolution in most scenarios, but this would also depend on the screen size/type).
Full High-Definition (FHD) : 1920 x 1080 pixels
4K Ultra High-Definition (4K UHD) : 3840 × 2160 pixels
8K Ultra High-Definition (8K UHD) : 7680 × 4320 pixels
There are typically two screen setups: an all-in-one "System on Chip", like an LG or Samsung Tizen, where the screen and digital signage hardware components are packaged up in one device (similar to a standard television), and a standalone unit that connects to a separate screen via HDMI cable, such as a BrightSign or Windows device.