how do I cope with those feelings?
There are various coping strategies, involving ways of justifying his and your behavior, as well as detaching from the issue and refocusing on other matters. I would recommend a blend of these approaches. Success will depend on the ability to realize several points:
Every person comes to a workplace with their unique work style, attitude toward the subject matter, and personal priorities, including life/work balance, responsibilities outside of work, interests, etc. Some people work to live and some live to work. Interpreting work as a productivity race against the other guy means not acknowledging and accepting this reality. No matter how hard you work, someone is always working harder and achieving more. Your workaholic colleague may be racing against someone, too... This is his personal issue. If you want to play catch-up driven by guilt, you can do that. Or, you can appreciate his productivity, but not let it be a standard for your own performance.
What matters is not your colleague's performance, but your performance relative to your job description. In assessment this is thought of as "norm referenced" and "criterion referenced" tests. Your perception of your performance should be criterion-referenced, i.e. based on fixed standards (i.e. your goals in performance review, job duties, quality of work based on standard accepted measures). Pegging your performance to that of another individual makes it norm-referenced, i.e. subjective and relative. This is an easy psychological trap to fall into since our brains are great at making comparisons, and comparisons with other humans (as opposed to written or numeric criteria) are natural and unavoidable. The trick is to discipline your brain, by consciously refocusing the object of the comparison from your peer to other explicit/documented criteria.
Just as you are experiencing guilt about not working as much in relative terms, the workaholic colleague may be a workaholic because of a variety of factors. Keep in mind that the reasons he gives may not be the actual reasons, but merely socially accepted reasons which are considered appropriate justifications, and which he has internalized. Without getting his perspective it is a guess what his actual motives may be, and I recommend sparing yourself this guessing game. A more useful approach here is to let it go, i.e. practice intentional detachment from both his behavior as well as reasons for it. Rather than lamenting the things you are not doing at work, appreciate and find joy in the things that you do get to do, by not working as much. These may be personal side projects, family time, interaction with friends and relatives, self-development and spiritual growth, learning new things and skills, pursuing passions, hobbies, or honorable causes like volunteering or charity.
There will always be more work to do, and you can never do all of it or get even close. But your parents and other loved ones do get older with each day, and before you know it they may not be able to give you their time and share and enrich your life in the same they they may be doing now. Same goes for friends and anyone else who you care about and who cares about you. Same goes for your time and energy, your ideas, ideals, and passions. You can always feel jealous of someone's ability to do something better than you, and there is always room for some healthy friendly competition in the workplace. But letting it consume you and take more of your mental focus than you wish it did can do more harm than good.
There is an incredibly rich world out there outside of work, and my sense is that all too many people get caught up in what happens within the office walls, at the expense of simply being, living in, discovering and enjoying this world. There have been some interesting survey studies of people on their death beds, and what they wish they had done more of when they were younger and healthier. Hardly anyone says "I wish I had spent more time in the office." I keep this in mind every day on my way to work, and it helps me keep my internal compass focused on the things that really matter, so that I don't regret not dedicating enough of myself to non-work-related pursuits years from now, when it may be too late. Good luck!