The first method gives you the ability to control (e.g. set the Level of) the logging on a per class basis. This comes at the cost of having lots of Logger instances.
The second method gives you a single Logger instance, but only allows you to control
logging for your entire application.
AFAIK, in a long running application, the only ongoing cost of having lots of (static) Logger instances is a small delta in memory usage. So this is a trade-off between a small increase in memory usage and flexibility / configurability of your application's logging.
While I wouldn't go so far as to create a Logger in each and every class, I think that you (or your users/clients) could come to regret it if you used just one Logger in your entire application.