I looked at both of these machines before going with the Stringway. I've had it almost a year now and love it. I didn't go with the Eagnas because I heard horrible things about their customer support. The guys at Alpha (US) as well as Frank in Europe were great with any questions/concerns I ever had with my Stringway. As with most things, you get what you pay for. I'm sure there are reasons why the Eagnas is so much cheaper....I just didn't want to find out why!
The only thing I don't like about my machine is that sometimes I have issues with clamping the very top/bottom cross on Wilson tennis racquets, and the same for almost all badminton racquets. Also, the tension head is sometimes far away from the frame, so make sure you use a bit more string than is recommended unless you want to use a starting clamp as a bridge....which isn't a big deal.
I used a Ektelon H previously, and I would say this machine does a better job, but it is a bit slower to use.