What's better, a full or partial length orthotic?

To a large degree, this falls under preference rather than right or wrong.  There are advantages to both styles.  Whenever possible we suggest that your Doctor go with a full length orthotic because it will not slide or shift in your shoes and therefore is more efficient.  With that being said, a possible disadvantage of a full length orthotic may arise when switching from shoe to shoe because the shape of the toe area varies from one shoe to another and whereas the orthotic may fit perfectly in one shoe, it may not fit into another shoe you may wish to wear.
Conversely, a partial length orthotic does not have this issue and can be easily transferred from shoe to shoe.  However, this style may have a tendency to shift or move in the shoe until it has been worn for a time and allowed to "settle into" the shoe.  This is usually only a factor in the first week or two of wear. 
The advantage of being able to wear an orthotic in various shoe or sneaker styles does have limits.  An orthotic made for some shoes will function differently than an orthotic made for a sneaker.  Orthotics made for dressy or fashionable styles are often too narrow to function correctly in what usually is a larger sneaker, work boot or conservative dress shoe.  This is why many people ultimately get more than one pair of orthotics as they do not like to go without the support and comfort that the orthotics provide for any length of time.