To determine if the user is logged in at all, you'll want to use the currentUser variable:
{% if currentUser %}
Welcome, {{ currentUser.friendlyName }}!
{% endif %}
To determine if the logged in user is a specific user, then simply compare against their username:
{% if currentUser and currentUser.username is 'johndoe' %}
Hey Johnny Boy!
{% endif %}
The isCurrent method is useful when targeting a more generic UserModel (where you don't know if the user would be the current user).
{% for user in craft.users %}
{% if user.isCurrent %}
{{ user.friendlyName }} is you!
{% else %}
{{ user.friendlyName }} is someone else.
{% endif %}
{% endfor %}