Writing – How to Start a Letter to Two Persons

Note that, in all cases here, it is assumed that you want to address both equally. Keeping that in mind, I would say that your first sentence is the better choice, unless:

The persons share a surname: for example, if you are writing to a married couple you may wish to address them as:

Mr and Mrs Smith
Mr and Mrs J Smith
Mr and Mrs John Smith

Note that, when including a forename, it is generally the name of the husband that is used. In the case of a same-sex marriage or partnership, you might include both forenames, or the initials of each person:

Mr J and Mr A Smith
Mr John and Mr Alan Smith

Ms J and Ms E Smith
Ms Joan and Ms Elaine Smith

There are more than two persons addressed: in which case, you should not use "and" between each name. Rather, you should use a comma between each name but the last. If you want to, you might include the Oxford comma on the second-last name:

Mr J Smith, Mrs N Jones and Mr A Cartwright (no Oxford comma)
Mr J Smith, Mrs N Jones, and Mr A Cartwright (with Oxford comma)

There is also a (slightly archaic) way of addressing two or more men. You wouldn't use this in general day-to-day writings, but I wouldn't be surprised to learn that it's still used in some formal settings:

Messrs Smith and Cartwright
Messrs J Smith and A Cartwright
Messrs John Smith and Alan Cartwright

Another thing you will want to consider is whether you are using the correct salutation, as this can affect how you address someone. If you use "dear," you would generally not include the forename of the addressee.