# same result

bash-4.2$ [[ 'test' == ?e* ]]; echo $?
0

bash-4.2$ [[ 'test' == ?x* ]]; echo $?
1

bash-4.2$ [[ 'test' =~ .e.* ]]; echo $?
0

bash-4.2$ [[ 'test' =~ .x.* ]]; echo $?
1

# but at different speed

bash-4.2$ time for x in {1..1000000}; do [[ 'test' == ?e* ]]; done

real    0m4.943s
user    0m4.899s
sys     0m0.011s

bash-4.2$ time for x in {1..1000000}; do [[ 'test' =~ .e.* ]]; done

real    0m17.056s
user    0m16.962s
sys     0m0.010s

# measure the loop's own speed to subtract it

bash-4.2$ time for x in {1..1000000}; do :; done

real    0m4.357s
user    0m4.329s
sys     0m0.009s

# to find out the times actually spent for matching
# - [[ 'test' == ?e* ]]   4.943 - 4.357 =  0.586
# - [[ 'test' =~ .e.* ]] 17.056 - 4.357 = 12.699