can you explain about being off by 5 minutes? do you mean, if it's 5:00pm, your mom's Rolex will say it's 4:55pm? As for servicing, how often and when do they know they need to have that done? thank you!
^ My DF's automatic watch is off by about 5 minutes and it so happens my mom's Rolex is off by 5 as well. Both wear their watches everyday. My watch is quartz and it keeps time quite accurately. Mechanical/automatic watches need to be serviced every so often while quartz/battery operated watches need their batteries replaced every 4 or so years. If your #1 concern is accurate time keeping, I would go for the Omega.
If you don't care for the movement of the watch and what lies underneath the case, then a quartz watch would be the best investment. There's no use paying extra for an automatic watch otherwise!