Hi Julie,
Since you've never had either one, you'd probably enjoy the Swedish more. It is a relaxing, invigorating massage. That sounds contradictory but when you experience it, you'll know what I mean.
The deep tissue massage is excellent for fixing problems that are locked into the tissue. Great results can be had with it.
But, you should treat yourself to the Swedish first before delving into the deep end...unless you have a specific problem you're trying to address, such as a medical massage issue.
The best to you.
Kelley