If I try to explain this, it will be very hard to understand, so I'll give an example. This example will be in pvp/bh, meaning that everyone pretty much has the same gear in p2p. Nobody will be in SS, claws, slayer helms, fire capes, infinity, etc. Every clan can afford ancients, ghostly robes, mystic robes, dds, etc. Richer people can return more, that's pretty much it.
Every member contributes up to 100% to the clan
In f2p:
Gear: 20%
Stats: 20%
Skill: 60%
In p2p:
Gear: 30%
Stats: 30%
Skill: 40%
This is just a rough example, there's no evidence backing up these numbers, it's just to serve as an example. The reason why some people believe f2p takes more skill is because they look at it relatively instead of absolutely. So I'll give an absolute analysis.
F2p:
Gear:20%
15%-Full iron with scim/bow
20%-Bind or mith
Stats:20%
15%-70+stat
20%-maxed out pure
Skill:60%
50%-Masser
55%-Knows how to dd
60%-Perfect at tanking,spamming,piling,etc
p2p:
Gear:30%
20%-Brings one style with straight food
25%-Brings one style, maybe with a KO wep, with combo food
30%-Brings a KO wep, best food, necks, brews, the works
Stats:30%
20%-70+stat
30%-maxed pure
Skill:40%
10%-Attacks people, woop tee doo
20%-Gets on piles, spams, tanks a bit
30%-Very effective at warring
40%-Tanks 10 ppl at once, KOs perfectly each time, etc
What I'm trying to say with this example is yes, p2p does incorporate a bit more on cash and stats, but very little. For cash, the most expensive gear is like ancient staff, barrages, mystic robes, and dds. It's more expensive than f2p, but most people can still afford p2p return sets. There not many out there that can afford to return in f2p but can't in p2p. For stats, in both f2p and p2p, the damage is linearly dependent on your stats, so it affects f2p and p2p the exact same. The only reasons why I weighted it more in p2p is that not everyone has 94 mage to barrage, and barrage is a bit better than burst. As for skill, there's just so little you can do to make a difference. There has never been a single f2p fight in BH/PVP where the smaller clan won. The most a single individual can put on his plate is showing up; all his other skills only give a slight edge. 50 of the most experienced pures will probably be evenly matched with 60 crappy pures in f2p. In p2p, it's completely different. Yes, cash and stats make a slightly bigger difference, but your skill makes a huge difference. With even levels and gear, I'd say 30 experienced p2pers can be matched up against 60 non-experienced p2pers. Even though there's relatively less skill involved in p2p, there is absolutely more skill involved. In p2p, the static variables of gear, stats, and numbers have an affect, and skill does as well. In f2p, just numbers affects pretty much everything. There is very little to be gained from being skilled.