All the electrical linear servos I know are using electrical motor. They transform the rotary motion of the motor into translating motion through a screw jack system.
With this type of technology you have to choose between power or speed ( ie depends on the screw pitch ).

For example, the Firgelli PQ12f is a high force linear servo that has a speed of 7mm/s.

Lets compare it to the Jr3421 which weight and size are comparable ( 25 grs vs 19 grs and 33,02 mm x 14 mm x 25 mm vs 36,5 mm x 15mm x 22mm )

The PQ12f will output 15N at 20 mm or 30N.cm
The JR 3421 will output 65oz/in or 45N.cm in the same conditions.

The PQ12f has a linear speed of 7mm/s
The JR 3421 has a linear speed at 1 cm of 10 mm in 0,18 s ( two 30 degrees segments in 0,18 s ) or 33 mm/s.

So for comparable torques ( although the JR servo is 50% torquier ) the rotary servo is 5 times faster than the linear one.
This type of linear servo would be simply useless in a jet aircraft ( too slow or too weak ).

Airbus has been striving for a long time to fit electrical linear servos in their aircraft. The technology has not yet been able to offer acceptable solutions for fast applications.
Hydraulic screw jacks are used for stabilizer trim purposes at the present time.