Bash-completion is broken:

"echo $HOME/<TAB>" becomes
"echo \$HOME/" instead of listing all the files in $HOME
notice the added "\" before the "$".

In el6, "echo $HOME/<TAB>" results in "echo /home/username/", second <TAB> yields the list of files. This is okey. (bash-completion is not installed)

In el7, "rpm --erase bash-completion" restores sensible behaviour:
"echo $HOME/<TAB>" yields the list of files in $HOME.

[root@titan00 ~]# more /etc/redhat-release 
CentOS Linux release 7.2.1511 (Core) 
[root@titan00 ~]# rpm -q bash
bash-4.2.46-20.el7_2.x86_64
[root@titan00 ~]# rpm -q bash-completion
bash-completion-2.1-6.el7.noarch

K.O.