In a simple case like this, the only difference is that the masu-stem sounds more formal.
In a more complex sentences, te-forms and masu-stems can coexist. In such cases, I think te-forms tend to be used to describe a sequence of events, whereas masu-stems tend to be used to list things in parallel.
In this example, both sentences are correct, but Sentence 1 feels more natural and sophisticated than Sentence 2:
(This may be obvious to you, but note that masu-stem and te-form are basically different concepts, and they are usually not interchangeable in most other cases. For example, subsidiary verbs only follow a te-form.)