Both burn natural gas to make electricity. The choice depends on size, climate and how the site runs.
Gas engine gensets are large piston engines, typically 1–19 MW per unit (e.g. Jenbacher J620 at 3.5 MW, Wärtsilä 20V34SG at 9.8 MW). They have high simple-cycle efficiency, hold output well in hot weather, and run on low-pressure gas. Many small units make N+1 redundancy simple: one can be down for maintenance while the rest run.
Gas turbines are more compact per megawatt and need less frequent maintenance. Aeroderivatives (e.g. GE LM2500XPRESS at ~35 MW) start fast; industrial turbines (e.g. Siemens SGT-800 at up to 62.5 MW) suit continuous duty and CHP. Turbines lose output as temperature rises above 15 °C and aeroderivatives need high-pressure fuel gas.
Rule of thumb: for hot sites under roughly 100 MW that need redundancy, engines often win. For larger sites, CHP or where space is tight, turbines often win. Many buyers who ask for turbines actually need megawatts; considering both widens the supply.