To create an all-time team for both BYU and Utah football, I'll select players based on their historical impact, records, and accolades at each position for both teams. Then, I will provide an analysis on how the match-up might play out based on these selections.

### All-Time BYU Football Team

**Offense:**
- **QB**: Ty Detmer (Heisman Trophy winner, 1990)
- **RB**: Luke Staley (Doak Walker Award winner, 2001)
- **WR**: Austin Collie (All-time leading receiver, NFL career)
- **WR**: Eric Drage (1st team All-WAC, 3,000+ yards)
- **TE**: Gordon Hudson (Consensus All-American, College Football Hall of Fame)
- **OL**: John Tait (All-American, 1st round NFL draft pick)
- **OL**: Bart Oates (NFL Pro Bowl, Super Bowl champion)
- **OL**: Mo Elewonibi (Outland Trophy winner, All-American)
- **OL**: Ryan Denney (All-Conference, NFL career)
- **OL**: Travis Bright (All-Conference, NFL career)

**Defense:**
- **DL**: Ezekiel Ansah (Top 5 NFL draft pick, Pro Bowl selection)
- **DL**: Jason Buck (Outland Trophy winner, NFL career)
- **DL**: Jan Jorgensen (All-time sack leader at BYU)
- **LB**: Kyle Van Noy (All-American, NFL Super Bowl champion)
- **LB**: Fred Warner (NFL Pro Bowl, All-Pro linebacker)
- **LB**: Shay Muirbrook (Defensive leader in sacks, key to 1996 team)
- **CB**: Derwin Gray (All-Conference, NFL player)
- **CB**: Tim McTyer (All-WAC, NFL career)
- **S**: Tom Holmoe (All-WAC, NFL Super Bowl champion)
- **S**: Daniel Sorensen (NFL career, Super Bowl champion)

### All-Time Utah Football Team

**Offense:**
- **QB**: Alex Smith (No. 1 overall NFL draft pick, Heisman finalist)
- **RB**: Zack Moss (All-time rushing leader at Utah, NFL career)
- **WR**: Steve Smith Sr. (NFL Pro Bowler, one of the best WRs in NFL history)
- **WR**: Kevin Dyson (NFL career, remembered for the "Music City Miracle")
- **TE**: Dalton Kincaid (1st round NFL pick, All-Pac-12)
- **OL**: Jordan Gross (All-American, NFL Pro Bowler)
- **OL**: Garett Bolles (NFL 1st round pick, Pro Bowler)
- **OL**: Zane Beadles (NFL starter, All-Pac-12)
- **OL**: Tony Bergstrom (NFL career, All-Conference)
- **OL**: Isaac Asiata (All-Pac-12, NFL career)

**Defense:**
- **DL**: Luther Elliss (All-American, NFL Pro Bowler)
- **DL**: Star Lotulelei (First-round pick, dominant DT in college and NFL)
- **DL**: Bradlee Anae (All-time sack leader at Utah)
- **LB**: Devin Lloyd (All-American, NFL career, 1st round pick)
- **LB**: Luther Elliss (NFL Pro Bowler)
- **LB**: Jason Fanaika (All-Pac-12, NFL career)
- **CB**: Eric Weddle (NFL All-Pro, Super Bowl champion, one of the best safeties in NFL history)
- **CB**: Sean Smith (NFL career, Pro Bowler)
- **S**: Marcus Williams (NFL career, ballhawk safety)
- **S**: Marquess Johnson (All-Pac-12, NFL career)

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### Simulation Breakdown:

- **Quarterbacks**: Ty Detmer vs. Alex Smith – Detmer was a prolific passer with a Heisman Trophy, but Smith’s efficiency and mobility in Urban Meyer’s spread offense would make him a dual-threat. This position could be a toss-up based on system preferences, though Smith's athleticism might give him a slight edge.

- **Running Backs**: Luke Staley vs. Zack Moss – Both backs were elite for their teams, but Moss’s durability and all-time rushing record give Utah an advantage in the ground game.

- **Receivers**: BYU's Collie and Drage were dominant in college, but Utah's Steve Smith Sr. stands as one of the best NFL receivers ever, giving the Utes a big advantage here. Kevin Dyson's NFL experience also adds to Utah’s edge.

- **Tight Ends**: BYU's Gordon Hudson was a game-changing player, while Utah's Dalton Kincaid had a strong career. BYU likely has a slight edge in this position due to Hudson's historical dominance.

- **Offensive Line**: Both teams feature elite linemen, but Utah’s more recent NFL success stories like Jordan Gross and Garett Bolles give them the advantage in the trenches.

- **Defensive Line**: Utah's line, anchored by Star Lotulelei and Bradlee Anae, would provide a formidable front. BYU has talent here, but Utah’s size and strength might overpower them.

- **Linebackers**: Both teams have great linebacker talent, but BYU's duo of Van Noy and Warner, both successful in the NFL, gives BYU an edge in versatility and pass coverage.

- **Secondary**: Utah’s secondary with Weddle and Marcus Williams is likely stronger. BYU’s defensive backs have NFL experience, but Utah’s players were more impactful at the NFL level.

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### **Who Wins?**

Utah's defensive front and secondary give them a significant advantage in stopping BYU’s passing game, while Alex Smith's mobility and Zack Moss’s ground game could exploit BYU’s defense. However, BYU's dynamic passing attack, led by Ty Detmer and its talented linebackers, might keep the game competitive.

**Final Verdict**: In a close simulation, Utah likely wins by a narrow margin, largely due to their stronger defense, offensive line, and more explosive wide receivers. Score prediction: **Utah 31, BYU 27**.