This is a loaded question as there are many considerations. Locality issues are one. In my area for years ATT has had the best coverage. Verizon was second fiddle BUT Verizon towers were powered the longest in the aftermath of a hurricane in 2004 when ATT towers went down. Point? Locally you will get varied responses from region to region. CDMA systems travel greater distance but also have singular use- voice or Internet but not at the same time, locked equipment and no Europe. This includes just about every carrier but ATT and TMobile.
You have to research your options for sure and most likely have a backup plan of communication is critical. Sprint has the most options available and I would recommend them as a backup for you using one of those pay as you use options like Tang. That way you also get tethering, etc. for really cheap OR Internet on the GO at Walmart where you pay WHEN you use it and loose no minutes, etc. The catch is the carrier signal strength. I would also purchase a cell phone signal booster with max antenna.
My first camping trip I had no WiFi or phone signal. After installing a booster and WiFi signal system (WiFi Ranger) I no longer have many issues using Sprint or ATT. One usually works at least.
Europe is GSM (ATT or TMobile) but then again, not all is happy. You have to purchase a phone that is compatible with various bands, etc. More research.
Sometimes the least route of resistance on something like this is to have multiple products. TO keep my costs down, I dropped ATT with my ATT iPhone when out of contract, joined StraightTalk with my GSM phone and now have unlimited talk, text and data for $47 versus $98 for 450 min talk, 1500
text and 2gb data. Get this, as soon as my phone activated I was right back on the ATT network! They use Verizon, TMobile or Verizon as their network partners. The support is not that good if you have to call but I do not call that often. I highly recommend them. You can bring your Verizon or ATT phone over to them. If you need to buy a phone it will be expensive (unlocked) but you will save in the long run. My new iPhone was $599 I believe rather than $299 for the subsidized price under contract. In a year's time though I save $612 for the service.