Speed of Update

The most significant advantage of using Spigot is that it updates faster. When new Minecraft versions release, you can generally use Spigot within a few hours. Paper often takes a few hours to days beyond Spigot, as Paper must wait on Spigot to update before starting. If updating your server straight away is highly valuable to you, Spigot may be a good idea. This drawback may disappear in the future due to Paper's plans on becoming a hard fork.

It's worth noting, however, that it's unwise to update to a new version of Minecraft within the first week. During this time, Minecraft, Spigot/Paper, and plugins are often not yet stable. Instead, you could use a plugin that allows newer versions to connect to older servers, such as ViaVersion, temporarily. Once the new version is stable, you should update to keep up to date. It would be best if you did not use ViaVersion in the long term.

Vanilla Dupe Bugs

For some server types such as Anarchy, retaining various duplication exploits may be wanted. Paper patches any known dupe bugs, meaning it could interfere with wanted gameplay. Dupe bugs are also generally unable to be re-enabled on Paper, unlike all of their other behaviour changes.

Better Performance

The main benefit of using Paper is the significantly improved performance compared to a Spigot or CraftBukkit server. Paper includes a large number of changes that speed up different aspects of the game. It's impossible to give exact performance statistics due to how different every Minecraft server is. However, it's common for Paper to increase the number of players your server can support without slowing down by over 50%.

Paper also includes many options that you can enable to further improve performance at the expense of impacting gameplay behaviour. Such as optimising the way the game chooses spawn locations for mobs to allow fewer overall mobs without players noticing.

Paper-Specific or Paper-Improved Plugins

Paper adds many features to the API, allowing plugins to do more things on the server. While many of these are performance-focused, some also improve functionality. Due to this, many plugins recommend using Paper for improved performance or functionality.

While somewhat rare at the moment, there are also a small number of plugins that require using Paper rather than just using Paper when available. For example, the upcoming CraftBook 5 depends on Paper. There are a few things that are impossible for a plugin to do on Spigot. Suppose the functionality of a plugin only works on Paper. In that case, it doesn't make sense for the plugin to support Spigot at all. As Paper supports Spigot and Bukkit plugins, but Spigot doesn't support Paper plugins, this means that Paper has a more extensive (albeit not by much) plugin base.

Larger Community and Community Focused

More servers use Paper than Spigot, meaning it has a broader community. More people using the software means bugs are found and fixed more quickly, and more people want to contribute to the project. A wider community also means that more people can help when something goes wrong.

Paper is also more community-focused, regularly conversing with other sections of the Minecraft community such as Sponge and Fabric to share discoveries and improvements. The development process is also public, so anyone can help out if they can do so, including the update process for new Minecraft versions.

Timings 2.0

Paper includes an improved version of the Timings software that Spigot has. The improved version is much faster and provides more accurate and detailed information. While Timings isn't perfect, it's a handy tool to get a general idea of performance issues when used correctly.

Patches Bugs

While potentially a downside for some, Paper patches many bugs that can heavily impact servers. Paper aims to fix every known item or block duplication bug, which lets servers ensure that their survival gameplay is fair and free from cheaters. Generally, all changes that impact gameplay other than patches for dupe bugs will be optional.