Firstly let me say that both are great, great players. I don't want that to get lost in this debate.
I believe that Samuel Eto'o was the better player and striker. For me Eto'o was the best striker in the world from 2005-2010, and arguably still is the best striker in the world, it could be argued still for him for that accolade.
Henry was more versatile but this doesn't mean he was the better player, it just means that he was effective in each position he was deployed at.
Eto'o to me was the perfect striker. Pace, energy, intelligence, finishing, dribbling and most importantly, which imo, Henry lacked, Mental Toughness. Eto'o exuded all those attributes and more for Barca. He in terms of being the goal threat, was Barca's main man. Yes he had brilliant support in Ronaldinho, Deco, Xavi et al, but it takes two to tango. He had to get into those positions, he had to read the play and he used his ability to take advantage of that. Eto'o for that period was the most lethal striker in the world. One chance it all it took for him.
Eto'o never carried Barcelona but Henry never, EVER carried Arsenal. Just wanted to clear that up. Arsenal of that period are not the Arsenal you see now with RVP carrying them. Arsenal had a great back 4, Pires and Vieira and Gilberto in midfield and Henry had the best partner he could ever wish have wanted in Bergkamp. It was Bergkamp's intelligence, Bergkamp's brilliance that created many goals for Henry. So please Henry did not carry Arsenal.
People will go one to say well look at their stats and Henry had more goals and assists. This is not taking into consideration two very important things. One Eto'o spent 2000-04 at Mallorca, a mid table side at best and goal scoring opportunities being created would have been minimal. Therefore the chances for Eto'o to score or assist would have been way smaller compared to Henry at that time. Secondly from 2000-04 Arsenal were either the best or 2nd best team in England - by a country mile and particularly from 02-04 Arsenal had one of the best teams around and chances created were the highest in the league, thus Henry had plenty of chances to score and get his assists up.
There is also the opinion that because Henry played on the wings at Barca this could possibly make up for this. But let us not kid ourselves by suggesting that playing on the wings at Barca in 08,09 was the same as playing on the wings at any other club. Henry was never a conventional winger at Barca and you all know this.
Also I do not believe Henry had the mental toughness nor the bottle that Eto'o displayed. On numerous occasions (Many CL games, 2001 FA Cup final, important league games) Henry bottled it for Arsenal. Also was it a coincidence that when Henry was made leader of Arsenal, Arsenal never won a trophy?
Eto'o never bottled game (that I saw) He showed his mental toughness on the big occasions moreso than Henry.
This is why to me Eto'o will forever be the better player than Henry.
But please remember my first sentence. Henry is a great, great player and that for me is not up for debate.