When comparing Multibit vs Bitcoin Core, the Slant community recommends Bitcoin Core for most people. In the question“What are the best Bitcoin wallets for Windows?” Bitcoin Core is ranked 3rd while Multibit is ranked 4th. The most important reason people chose Bitcoin Core is:
Being open source allows the client to be peer reviewed. It also allows you to download the source code and compile it yourself in case you're worried that the source code is different from the distributed version of the application.
Ranked in these QuestionsQuestion Ranking
Pros
Pro Handles access to same wallets by multiple instances of the program well
Pro Allows having multiple wallets open at once
Pro Open source
Being open source allows the client to be peer reviewed. It also allows you to download the source code and compile it yourself in case you're worried that the source code is different from the distributed version of the application.
Pro High level of security
No third-party has access to your private keys. Private keys are both generated and held locally. Additionally, as it is the official client, it is the most actively peer reviewed wallet.
Cons
Con "Multibit is Deprecated - Do Not Use"
"Thus, KeepKey will discontinue support and maintenance of Multibit, effective immediately. We recommend that all Multibit users discontinue using it and you move your keys to other wallet software of your choosing." - https://github.com/Multibit-Legacy/multibit
Con You have to trust Multibit servers
As with all thin clients, you have to put some amount of trust in the servers that the wallet connects to for verification.
Con Initial sync takes a lot of time
Since the wallet downloads the entire blockchain the first time it loads, which as of July, 2020 is over 320GB, it can take a long time to download.
Con Takes up a lot of space
As of July 2020, the entire blockchain is over 350GB. The growth rate has been more or less linear for the last 5 years when it grew in size by about 200GB. Thus it's reasonable to expect the blockchain to grow to ~400GB by the end of 2020 and so on.