I went EMT-B to Paramedic (almost...I'm finishing the last 2 months of medic school right now). There are a lot of AEMTs in the class, but honestly, they don't necessarily get better grades than anyone else. There are plenty of labs at my school on IVs and most of my learning on how to do really good IVs in all sorts of locations and patients took place in a hospital clinical environment. Every nurse does it completely differently, and, after you're comfortable starting IVs, it's great to experiment with different techniques.
I had considered taking a phlebotomy class beforehand. Looking back, it would have been a complete waste of time and money.
The "leg up" that AEMTs really have is stuff like having a better understanding of scene command, ambulance operations, hospital transfers...basically they're generally a little more experienced...it doesn't mean that they have any better chance at passing or performing skills than you do. It does mean that they might be more experienced and might make a better medic on day one of their new job, though.
I'm just a student, but that's my current experience.