This answer is about bouldering vs rock climbing in gyms. Outdoor variations may be different.
Bouldering usually is more difficult and technical than rock climbing. The difficulty scales up much faster because climbs are quick and small. Plus you don't have to worry about harnesses. You just have to be brave enough to fall a few meters on a pad.
Rock climbing requires more grip endurance than bouldering. The easiest rock wall may use the same holds as the easiest boulder wall, but you still have to hold on for much longer.
Between the two, you may learn climbing technique a bit faster with bouldering. You also won't have to complicate your lesson with proper harness training. You can also assess your grip strength. If you can't hold on to a wall after a couple of climbs, then you probably wouldn't be able to complete a rock wall.
But also it's up to you. It's about having fun. Some people just prefer rock climbing. They like the challenge of reaching the top of a very high wall. Others prefer the technical challenge of figuring out a really tough boulder.
EDIT: One big advantage that others have stated is bouldering doesn't require a partner. Anytime after your lesson, you can just show up to the gym and practice.
There are gyms these days that have auto belaying systems systems that kind of act like a seatbelt. You just hook up and if you fall too fast it'll catch you and slowly lower you down. These don't seem to be common yet.