I absolutely agree with Bobbie. Her advice is pretty much what I would have shared.
Like her, I walked both. I walked CF in '05, CN in '10, CF in '12, and will return to the CN next June. Although the CN tends to bring longer days of walking for me, I finished in about the same time frame as the CF. I love the diversity of each walk, but would suggest the CF for my first walk. Since you'll be going in May, you'll miss the BIG crowds of later July/August.
I would also LOVE to do the Coast to Coast as you did. I guess in comparison, there will be much more people on the Camino than on that walk.
As for time, I think 5-6 weeks is sufficient for most, but this is totally up to you. For me, it took 28 days from SJPdP to SdC with one day rest. It took 29 days on the CN without a rest day from Irun to SdC. I also walk the 4 more days to Muxia and Finisterre. I would highly suggest this if you have the time.
Differences? I found the CN more more challenging and takes a bit more planning. Much more climbing. I also had many days of walking on tarmac and outrageous "detours" due to construction which almost always was a battle to get back to the route. There are much less refugios which makes for longer days of walking, but this is easily remedied by staying in pilgrim friendly hotels/pensions. On the CF, I average over 18 miles a day. On the CN, I walk almost 22 miles a day. It's much cooler along the coast of course with stunning scenery. The temptation to jump into the sea for a nice dip is great, and it's hard for me to get going again. I like to float. Oh, the seafood is incredible of course. Plenty of wine, good people, and pups to play with on each.
When I go back next summer, I'd like to combine the GR with the CN to stay more on trails and coast rather than "useless" detours.
Last, do a quick search here and see what others have come up with over the years.
¡Salud!
Simeon