Gridiorn, the brokers have a powerful system called ACATS, allows for the transfer of most positions in-kind plus cash in 3 business days or less. Far superior than the old DTC system.
I don't remember this part but ACATS might carry over the cost basis info as part of the transfer. Be sure to print out the tax basis report from E*Trade before initiating the transfer. Will save you time in case basis info don't carry over to your new broker.
Mutual funds are exempt from ACATS and takes longer to transfer due to the dinosaur shell account structure in most MF backshops.