There are a couple things that come to mind about what might be happening here in general:
- The sampling procedure behind the different modes (online, paper) may have been different. As a simple example of how this might have come about, if all employees with a computer were given the online survey and all employees without a computer were given the paper survey, it's easy to see why there would be large differences.
- Attitudinal questions are more sensitive to differences in survey administration than factual questions, because they don't represent a fixed or standard quantity - our moods are changeable minute to minute. Seemingly small things can have an impact on how participants respond, for example, the timing or environment. Surveys taken immediately after lunch, when the brain just got a nice rush of glucose, will probably reflect higher overall satisfaction. Surveys taken in group settings vs. individual settings may have different responses as social conformity may come into play.
On how to proceed....
Based on your description, it sounds like both effects are at play. Overall, my suggestion would be to take one action to correct what might be a major sampling effect, and then roll together the paper and online data for analysis.
Sampling effects for your situation: The online and paper surveys reached very different parts of the working population - those who use computers are typically going to be office workers and will be paid differently, be evaluated by their managers differently, work on different tasks, etc. Their responses to an employee survey would be expected to be very different. In addition to the survey targeting very different groups, the method by which you sampled the employees was different. 100% of computer-using employees received an invitation, vs. an unknown convenience sample of non-computer users. Their response rates may have been different.
Addressing sampling effects: The fact that online and paper populations are different types of employees and therefore respond differently is not a concern. They are different in reality and the survey data reflects that. If understanding these differences is valuable, it would be better to use a variable like "job category" or something if you collected that, but if not, you could keep the online/paper variable for analysis as a rough way to divide office and non-office workers.
The fact that different proportions of the relevant populations may have been reached is a concern - if all office workers responded, but only half non-office workers responded, then your office workers are over-represented. If possible I would try to weight the paper and online , by company, to the proportion of the relevant populations in each company. The fact that convenience sampling was used for paper surveys is unfortunate, as it may not represent the population, but I can't think of anything to do now.
Survey administration effects in your situation: There is likely some effect, but these will be hard to define and correct for. Online surveys were probably taken at the convenience of respondents at their desk, while it sounds like paper surveys may have been taken in a group setting at a set time. This probably has some effect on responses but would be difficult if not impossible to adequately define and correct for.