I used my Bionic all over the world; including Britian, Germany Taiwan Indonesia. It can even be made to work on ATT in the USA. I used it both with the Verizon SIM (Vodafone) and international sims. You can read about that here:
http://androidforums.com/motorola-d...an-do-cmda-4lte-gsm-hspa-image-intensive.html
but basically the Bionic could be hacked to be a fully unlocked GSM and LTE phone.
Right now I'm in Cayman with the RMHD. My understanding too is that the RMHD is sim unlocked for foreign countries and will only function in the US on VZW. As far as cost goes, here is my conclusion. If you mostly make calls over seas an international sim will likely be cheaper but you get a different telephone number of course. If you mostly text, then either way. If you mostly use data, then VZW is a pretty good deal.
Voice: VZW is about $2 per minute and most in-country cards will be less an include free incoming calls.
SMS: $.05 to receive and $.5 to send is about as cheap as it gets so VZW is competitive.
Data: Foreign sims often give very little data and these phones even on HSPA or even UMTS eat through data. I once turned my data roaming on in Taipei for a few minutes and went through half my data. On VZW if you plan to use data, you MUST subscribe to the data plan otherwise you will be charged $20/MB. This will instantly gets ultra expensive. However the data plan is only $25 for 100MB. That doesn't sound like much in the land of 2GB data plans but having 10 devices on our account I can tell you that most of our devices only use about 200MB/month. For email, map data and a bit of browsing it is plenty especially if it is a shorter trip.
If you use VZW's sim all you have to do is go to your "my Verizon" account on the web and enable global dialing which is a free feature.
For a different carrier, you would need a Micro sim for the RM and possibly APN data from the sim company to program into the phone so it knows how to use data and MMS.
I elect to use the VZW sim (service) because I decided it was too much hassle to swap numbers for short trips. If I was gone longer it might be worth it. Also my international sims are full size and I don't have a cutter to make it a micro for this phone. Most places I am staying have free wifi so data is not a problem and the occasional calls won't kill me. For longer calls back to the USA I either Tango (Skype) over wifi for people who have that or use my google voice number with the "Spare Phone" app (Grooveip, Talkatone, Skypeout) to place wifi calls to US numbers for free. If you want to conserve data and are driving a lot, you can precache google map areas within the app over wifi.