My reasoning for Federer (maybe someone else can break down Woods' resume):
* 15 Grand Slam titles since 2003, breaking Sampras' record of 14
* He won 3 of 4 Grand Slam titles four straight years (2004-07)
* He has beaten 11 players in Grand Slam finals
* In those 15 Grand Slam finals he has played 56 sets, and won 47 of them.
* Was the runner-up in 6 Grand Slams
* Won his first 7 Grand Slam finals
* The only player to win 3 Grand Slams finals at least 3 times
* Won 5 straight Wimbledon titles and 4 straight U.S. Open titles
* Won at least one Grand Slam title 7 straight years
* 188-27 record in Grand Slam tournaments (87.4%)
* Seeded No. 1 for 18 consecutive Grand Slams
* Two 27-match Grand Slam win streaks
* 40 straight wins at U.S. Open and Wimbledon
* Only player to win 19 straight matches on 3 Grand Slam surfaces
* Won his last 148 5-set matches after taking the first 2 sets
* 4 ATP World Tour titles
* Won 16 ATP World Tour Masters 1000 titles (2nd all time)
* The only player to win four ATP World Tour Masters 1000 titles in a season twice (2005–06). His 8 titles in two years, 11 in three years, and 13 in four years are record achievements.
* The first player to be ranked World No. 1 for four consecutive (non-calendar) years from February 2, 2004, to August 17, 2008
* The first player to be ranked No. 1 for 237 consecutive weeks, thus surpassing Steffi Graf for the all-time record of 186 consecutive weeks among all tennis players, male or female
* Won a record 26 consecutive matches against top ten ranked opponents
* Won 24 straight finals from the tournament in Vienna in October 2003 through the tournament in Bangkok in September 2005
* As of September 2009, has won 61 of 83 finals during his career
There are more stats, but you get the point.
Here are the awards he's won since 2003 (wikipedia)
2003
1. ATP European Player of the Year
2. Swiss Sportsman of the Year
3. Swiss of the Year
4. Michael-Westphal Award
2004
1. ATP European Player of the Year
2. ITF World Champion
3. Sports Illustrated Tennis Player of the Year
4. Swiss Sportsman of the Year
5. Reuters International Sportsman of the Year
6. BBC Overseas Sports Personality of the Year
7. International Tennis Writers Association (ITWA) Player of the Year
8. Golden Bagel Award
9. European Sportsman of the Year (aka UEPS [Federation of European sports journalists] Sportsman of the Year)[43]
2005
1. Ambassador of United Nations' Year of Sport and Physical Education
2. Goldene Kamera Award
3. ATP Player of the Year (for the year 2004)
4. Stefan Edberg Sportsmanship Award
5. ATPTennis.com Fan's Favourite
6. Laureus World Sportsman of the Year (for the year 2004)
7. Michael-Westphal Award
8. International Tennis Writers Association (ITWA) Player of the Year
9. International Tennis Writers Ambassador for Tennis
10. Most Outstanding Athlete by the United States Sports Academy
11. Freedom Air People's Choice Sports Awards International Sportsperson of the Year
12. ITF World Champion
13. ESPY Best Male Tennis Player
14. European Sportsman of the Year (aka UEPS [Federation of European sports journalists] Sportsman of the Year)[43]
2006
1. L'Equipe Magazine's Champion of Champions (for the year 2005)
2. ATP Player of the Year (for the year 2005)
3. Stefan Edberg Sportsmanship Award
4. ATPTennis.com Fan's Favourite
5. Laureus World Sportsman of the Year (for the year 2005)
6. ESPY Best Male Tennis Player
7. International Tennis Writers Association (ITWA) Player of the Year
8. International Tennis Writers Ambassador for Tennis
9. ITF World Champion
10. BBC Overseas Sports Personality of the Year
11. Swiss Sportsman of the Year
12. EFE's Sportsman of the Year
13. Golden Bagel Award
14. Most Outstanding Athlete of the Year by The United States Sports Academy
15. European Sportsman of the Year (aka UEPS [Federation of European sports journalists] Sportsman of the Year)[43]
2007
1. L'Equipe Magazine's Champion of Champions (for the year 2006)
2. ATP Player of the Year (for the year 2006)
3. Stefan Edberg Sportsmanship Award
4. ATPTennis.com Fan's Favourite
5. Arthur Ashe Humanitarian of the Year
6. Laureus World Sportsman of the Year (for the year 2006)
7. ESPY Best Male Tennis Player
8. ESPY Best Male International Athlete
9. ITF World Champion
10. BBC Overseas Sports Personality of the Year
11. Tennis magazine's 2007 player of the year
12. Swiss Sportsman of the Year
2008
1. L'Equipe Magazine's Champion of Champions (for the year 2007)
2. European Sportsman of the Year (for the year 2007) (aka UEPS [Federation of European sports journalists] Sportsman of the Year)[43]
3. Laureus World Sportsman of the Year (for the year 2007) – First ever winner of four Laureus World Sports Awards[44]
4. ATP Player of the Year (for the year 2007)
5. Stefan Edberg Sportsmanship Award
6. ATPTennis.com Fan's Favourite
7. ESPY Best Male Tennis Player
8. Swiss Team of the Year (with Stanislas Wawrinka as "golden team FedRinka")
2009
1. Stefan Edberg Sportsmanship Award
2. ATPWorldtour.com (formerly ATPTennis.com) Fan's Favourite
3. Talksport Hall of Fame
4. ESPY Best Male Tennis Player
5. Ehrespalebaerglemer award. An award given to outstanding citizens of the city of Basel.[45]