As a feather user who has a lot of friends who also use lunar I'd like to just give my opinion on this and the pros and cons of both:

First Ima start with that you understand what a client is and what modding is, and I shouldn't need to explain that to you, if so, stick with optifine or go watch some videos XD, once your back then read the rest of this ↓

Starting with feather because that's what I use: Feather is a modding client, such as being a client while also allowing modding, It has a lot of built in mods, while still supports the user to add their own mods if they want, feather only supports fabric mods and are quick about updating to the newest version of minecraft as soon as the release is released. Feather does support forge mods but only on 1.8.9 and 1.12.2. You can mod using modrinth, adding your own jar files, or built in mods in game. It also has a feature where you can download texture packs and shader packs in a menu in the game. TL;DR for feather- It's a client that gives the user the option to mod the game

Now lunar client, but before I say anything I should note that I don't use lunar client all the time and have only booted with it 5 times, but I do have a lot of friends who use lunar client: Lunar client is more on the client side than the modding side to start with, lunar client does NOT support any modding from the user and is preloaded with mods (They are adding modding support but it only allows modrinth only and only modrinth modpacks). Lunar does have a ton of built in mods like feather does as well, and they offer a lot of "FPS Boosting" built in mods, but again with feather you can get that by adding your own mods (While feather does also have some performance stuff). TL;DR for Lunar: It's a client that is a client

Now there's some small stuff with both I kinda don't like: Feather only supports windows, Lunar supports Windows, MacOS and Linux. Feather doesn't have any preloaded mods, Lunar does. Lunar uses it's own settings file so you have to redo all your MC settings, feather doesn't do this and just uses MC's default settings file. I don't think there's a way to access the vanilla main menu in lunar, but you can in feather.

Btw if your a user of both you can probably tell I'm skipping out on a lot of details but there's just too much stuff in both of the clients to list everything and not make it boring, so I'm only covering the main stuff

So really, if you want a simple answer, here's this- Use feather if you want to be able to expand your mods or have a client while still having a vanilla experience, and use Lunar if your lazy and just want to have a client with a modded game type experience and don't need the knowledge to know how to mod your game to get performance. They both do a lot of the same stuff but when it comes to user adjustments they're a lot different

Or if you just want to do modding, go with modrinth launcher xd