The Minecraft modding ecosystem massively changed with the release of Minecraft 1.13. Due to a long update cycle of Minecraft Forge, a few similar projects popped up to replace it in the meantime. Fabric, Rift, and a few other projects provided a lightweight mod loading framework in Minecraft Forge's absence. While the other projects did not gain a foothold after Minecraft Forge became available again, Fabric has cemented itself as a powerful modding platform in the community. Having been a while since Minecraft Forge was released, is Fabric still relevant?
It's essential to have a solid understanding of each platform to help decide which to use. Both are projects that allow installing mods on Minecraft clients or servers.
Minecraft Forge is a modding framework for Minecraft that provides many helpers to make writing compatible mods easier. This allows large modpacks to work coherently, with duplicate items and blocks not causing any issues. Forge also makes it easier to do common tasks such as creating new blocks, entities or listening to various game events. Due to Minecraft Forge being more extensive, it also takes longer to update, especially as Minecraft Forge developers are also the people who update MCP (Mod Coders Pack), one of the tools that let modders see the game code. MCP doesn't matter too much to users, but it is the platform that allows Minecraft Forge to modify the base game.
To summarise, Forge is best for ensuring that many mods work well together.
Fabric is a lightweight mod loader for Minecraft. While it provides optional packages to make it behave more like Forge, the primary purpose is to set up a simple environment in which mods can manipulate the game. Unlike Forge, Fabric does not offer any interoperability layers or helpers. Fabric's goal of remaining lightweight allows it to update very quickly, to the point that it can update to every Minecraft snapshot version. Although Fabric for snapshot versions exists, many mods are never made available for these versions. Fabric also makes fewer changes to the game and is, therefore, less prone to bugs.
Recently, many people have started using Fabric to run Minecraft Servers. Due to projects like Paper and Spigot modifying the behaviour of some complex Redstone contraptions, Fabric has found use amongst technical Minecraft players. Say you want to run a vanilla (normal Minecraft gameplay) Minecraft server with a few utilities to make running a server safer and more manageable. In that case, Fabric may be a good option.
To summarise, Fabric is best for running more lightweight mods.
There is no simple answer over which is better. Both platforms have their benefits and downsides, such as what platforms the mods you want to use are available on or if you wish to use many mods that add content.
If you're going to do something simple like using WorldEdit in singleplayer, Fabric is probably your better option. If, instead, you want to play with multiple mods that all add blocks and items, Forge is better suited to what you're doing. The most significant factor in the decision will be which one supports the mods you want to use. Not all mods exist for both Forge and Fabric, so you often do not get a choice. Mods that are much more suited to Forge, such as adding tremendous amounts of blocks, will most likely not provide a Fabric version.
As is generally the case, the answer is that it depends on what you're doing. One platform isn't better than the other; both Minecraft Forge and Fabric have their strengths and weaknesses and are suited for different circumstances.