While Verizon and Cricket are both CDMA networks, so they should work if you try to use the device on the other network, if the tablet itself is locked to a carrier/service provider (which happens when you buy it from a carrier/service provider) no matter what the person is telling you, it won't work on any other carrier/service provider until the original one unlocks the device.
Now if you owe funds to them for the device, say tablet not paid for and got a contract for it, or their new making payments on it thing, then they are not required to unlock it so it can be used on another network. Not until it is paid for.
I would first check with the carrier/service provider you want to change to and ask them if that particular device will work on their network. Always best to check. Then, if they say it can, and if you have fully paid for the device, then call your current carrier/service provider and tell them to unlock it.
Now if you didn't get the device through them, and you bought it on your own and then added a SIM to use their service, there should be nothing stopping you from getting a new SIM from a different carrier/service provider.