If swapping SIMs when you enter a new country is OK for you (and then taking the time to test, configure, and troubleshoot each new SIM as needed) then you can save a few bucks. One of the challenges in my search was finding a company that had good roaming rates in all three countries we visited, with Switzerland being the wild card. It seems that Switzerland is not supported as often or is more costly with some of the so-call pan-European SIMs I checked out. Maybe it's because they are on not on the Euro. But lefrenchmobile DID roam in Switzerland with reduced rates. There are a few others that include Switzerland, if you examine their web site for details. I'm not a shill for lefrenchmobile but lefrenchmobile company solved our roaming needs adequately with minimal confusion and good support.
If you only expect to make phone calls (voice-only) then your shopping is easiest. It gets more involved when you want voice, texting, and data (forget streaming, by the way). Data brings in another set of decisions. Then you'll want to factor in the countries you are visiting and does the SIM roam with good rates in all of them? Then you may want to examine the company and its varied plans, their costs, their duration and their plan's longevity. And: How easy is the web site to use? How do you top-up securely? Also consider if the company has English language phone support. Additonal factors may be how many plans can be in your account at a time and do you want a US phone number or local country phone number? Is call-back acceptable?
Confusing? YES! I suspect most people just take a company, any company, and go with it rather than slog though all these decisions. Usually, if your just grab any decent-looking SIM, you will escape most exorbitant roaming fees, but not always get the lowest price or best support. Maybe that's good enough. If so, stop reading here and get your SIM.
IMHO, here's the least time-consuming solution. After landing, go to a kiosk where they sell phones and SIMs - in good English. Tell them your exact needs and make sure what they sell you does all you expect. Hand them your tablets, phones, whatever and have them install the SIMs and TEST that everything is working to your heart's content. Assuming the seller is trustworthy, you should be able to walk away with a working solution. This may not be the cheapest solution, but it can be the quickest and easiest.
I'm am a computer tech and love hacking and testing and troubleshooting - but not while I'm touring, it's a waste of precious travel time. As a poster on tripadvisor pointed out, we sometimes spend a lot of time saving a few dollars on the smaller costs (phone and moblie data service) to the neglect of the larger costs (airline fares, hotel costs, meal costs, efficient itinerarys). My travel hour was worth between 35 to 50 dollars and hour for our recent trip. And we were traveling in a budget-oriented mode, a la Rick Steves. I'm glad I heeded that poster's advice and spent a few dollars more for a SIM that worked in ALL countries we would visit and had an easy to use website and plan selection.
We traveled with 2 "unlocked" GSM phones and two tablets for a total of 4 SIMs to manage. Even with lefrenchmobile, (which I believe is the easiest to understand and use) I spent an extra 2 hours at CDG troubleshooting my wife's so-called "unlocked" phone. After talking to lefrenchmobile's English free phone support (on my phone) they concluded that her phone was not really unlocked (even though it seemed to work with multiple SIMs in the USA). The time and money-saving solution was for her to walk around the airport looking for a true unlocked phone to buy. She spent 25 Euros on a decent cheapie and the lefrenchmoible SIM then worked in it. We were up and running and headed to Montmartre for the rest of the day.
I hope your phone and data experience is trouble-free and you spend more time touring and enjoying the sites!