I've had both.... if you do not want too much action like a controlled break stright up the center, phenolic is fine. I was told there are several phenolic tips and the linen based is better.
If you want lots of spin action Samsara's break tip is known for this, and I had one.
My cuemaker makes alot of break cues for some of the best breakers I have seen, and utilizes a compressed pigskin, with his "special secret mix" resulting a very hard tip.
I got tht tip and saw it tested against the phenolic I had..... it proved harder by bouncing higher off the ground when two shafts with the two different tips were dropped straight, vertical tip firs, from about 4 ft. high distance off the ground, to a cement floor. Ned Morris says his tips will last as long as the cue and take no maintenance.
I do not want much over action off my break.