As far as the coverage goes they are basically the same. When you (or your employer) stop paying or you leave your job, they are both done.
Your employer is buying the group policy sort of at the average rate for all employees, young or old, healthy or not so healthy. So, if you are healthy, don't smoke, have parents that lived to a ripe old age, you should be able to easily find term life insurance cheaper than the group rate. If you smoke and particularly if you have had a signifciant medical problem such as a heart attack or cancer, you may not even be able to get insurance except through your employer's group plan (or at least it could be very expensive). 14 years ago, I was diagnosed with cancer so the only place I could get insurance was through my employer. Now, after 14 years of being cancer free and a non-smoker, I qualify for a prefered rate with most insurance companies. (The way I see it, I cheated the insurance company out of at least 10 years of premiums).
Probably the biggest difference is in who owns the policy. The group policy is owned by your employer. Quit or lose your job, you lose your life insurance. Have your own term policy, the policy goes with you.
Another issue is a tax issue. If you buy a term policy, you will use your own post tax dollars. The group policy is usually an employee benefit and provided free to you up to some multiple of your annual salary. An employer can provide up to $50,000 of term life insurance tax free to an employee, any coverage over $50,000 the premium is taxable to the employee.
Bottom line, not knowing your circumstances, if you are healthy, buy your own term policy and take the employer policy up to the $50,000 limit. If you have a health issue and term insurance is expensive or unavailable, take as much of the employer's insurance as you can get. Try not to change jobs unless your new employer also has group life insurance.