Both feature Gen 1 Pokémon (LGPE includes Alolan forms and Megas). You can actually connect your Pokémon GO to Let's Go, transfer a Pokémon (only Kantonian, others will be hidden) over to Let's Go, and receive a Mystery Box in which you can catch Meltan for 30mins (unfortunately, after the 30 min lure, the box won't open for an entire week. Then, you restart the process again.). Also, both have the same feature of encountering Pokémon in the overworld and the possibility of them running away (like ... 'poof'), have candies that raise stats (in GO it allows them to evolve), and have size varieties.
Please note that Let's Go is "basically" a remake of Yellow.
GO: up-to-Gen 4 + starters of the Generation + mobile game
Let's Go: main series battle animations + Leveling Up + different starters + Switch branded game