Generally washing is seen to be more effective as there is less chance that germs will become immune to anti bacterial agents. Overall the findings seem to be that both options are roughly the same effectiveness.

All 18 classes and 360 students completed the study. Of the 3 students who withdrew, 2 did so because the soap was too irritating and 1 because both soap and hand sanitizer were too irritating. Absentee data are presented in Table 1. Data fi-om cohort A, phase 1 and cohort B, phase 2 were combined to form the Soap and Water Group. Data from cohort A, phase 2 and cohort B, phase 1 were combined to form the Hand Sanitizer Group. Absentee data from these two treatment groups are presented in Table 1. Both groups had 18 absences. The students' f-test was then applied. No significant differences were noted between the groups, indicating that the number of student absences was not appreciably affected by the hand-cleansing technique used

The claims that hand sanitizers remove 99.9% of bacteria would appear to be slightly creative. To start with how they work:

Hand sanitizers work by stripping away the outer layer of oil on the skin. This usually prevents bacteria present in the body from coming to the surface of the hand. However, these bacteria that are normally present in the body are generally not the kinds of bacteria that will make us sick.

Then the effectivness of hand sanitizers

She notes that the research shows that hand sanitizers do not significantly reduce the number of bacteria on the hand and in some cases may potentially increase the amount of bacteria on the hand. So the question arises, how can the manufacturers make the 99.9 percent claim?

How they can be advertised as removing 99.9% of bacteria

The manufacturers of the products test the products on inanimate surfaces hence they are able to derive the claims of 99.9 percent of bacteria killed. If the products were fully tested on hands, there would no doubt be different results. Since there is inherent complexity in the human hand, testing hands would definitely be more difficult. Using surfaces with controlled variables is an easier way to obtain some type of consistency in the results. But as we are all aware, everyday life is not as consistent.

Source for the above

There is some evidence that if you are trying to kill of a specific virus (e.g. the common cold) a hand sanitizer may be the better option.

Finally a quick quote about antibacterial soaps even though it wasn't a requirement for the answer.

Keep in mind that antibacterial soap is no more effective at killing germs than is regular soap. Using antibacterial soap may even lead to the development of bacteria that are resistant to the product's antimicrobial agents — making it harder to kill these germs in the future.

Souce here

Generally washing is seen to be more effective as there is less chance that germs will become immune to anti bacterial agents. Overall the findings seem to be that both options are roughly the same effectiveness.

All 18 classes and 360 students completed the study. Of the 3 students who withdrew, 2 did so because the soap was too irritating and 1 because both soap and hand sanitizer were too irritating. Absentee data are presented in Table 1. Data from cohort A, phase 1 and cohort B, phase 2 were combined to form the Soap and Water Group. Data from cohort A, phase 2 and cohort B, phase 1 were combined to form the Hand Sanitizer Group. Absentee data from these two treatment groups are presented in Table 1. Both groups had 18 absences. The students' t-test was then applied. No significant differences were noted between the groups, indicating that the number of student absences was not appreciably affected by the hand-cleansing technique used.

The claims that hand sanitizers remove 99.9% of bacteria would appear to be slightly creative. To start with how they work:

Hand sanitizers work by stripping away the outer layer of oil on the skin. This usually prevents bacteria present in the body from coming to the surface of the hand. However, these bacteria that are normally present in the body are generally not the kinds of bacteria that will make us sick.

Then the effectiveness of hand sanitizers:

She notes that the research shows that hand sanitizers do not significantly reduce the number of bacteria on the hand and in some cases may potentially increase the amount of bacteria on the hand. So the question arises, how can the manufacturers make the 99.9 percent claim?

How they can be advertised as removing 99.9% of bacteria:

The manufacturers of the products test the products on inanimate surfaces hence they are able to derive the claims of 99.9 percent of bacteria killed. If the products were fully tested on hands, there would no doubt be different results. Since there is inherent complexity in the human hand, testing hands would definitely be more difficult. Using surfaces with controlled variables is an easier way to obtain some type of consistency in the results. But as we are all aware, everyday life is not as consistent.

Source for the above

There is some evidence that if you are trying to kill off a specific virus (e.g. the common cold) a hand sanitizer may be the better option.

Finally a quick quote about antibacterial soaps even though it wasn't a requirement for the answer.

Keep in mind that antibacterial soap is no more effective at killing germs than is regular soap. Using antibacterial soap may even lead to the development of bacteria that are resistant to the product's antimicrobial agents — making it harder to kill these germs in the future.

Source here