They are different in terms of reload time, however, they are not different in terms of damage done per hit. The differing reload times will make for an effective difference in DPS though. Melee weapons will one-shot all Common Infected on all difficulties. They will also one shot all Special Infected on all difficulties, except for the Chargers (2 hits), Witches (4 hits), and Tanks (20 hits).
The following is a table in ascending order of rate of fire.
Weapon Hit time
Nightstick .650 sec
Machete .675 sec
Katana .750 sec
Golf Club .750 sec
Frying Pan .800 sec
Crowbar .830 sec
Guitar .830 sec
Baseball Bat .850 sec
Cricket Bat .850 sec
Fireman's Axe .910 sec
The Chainsaw is a special case, and it does 100 damage per hit and hits every .1 seconds for 1,000 DPS. All other melee weapons do 500 damage per hit (as calculated on the L4D wiki for the Level A Charge achievement).
Information is from the individual pages of the Melee Weapons on the L4D wiki, which I conglomerated here. Unfortunately, they don't seem to have any information on Gnome Chompski's reload time. :(
A lot of the information you're after is already covered on the other question/answer so I'm not going to duplicate it here. In regards to which melee weapons have the largest swing arcs and which reach the furthest, the obvious choice for both is going to be the Katana with the worst being the Nightstick.
Weapons with a large arc allow you to hit multiple infected with a single swing, weapons with a larger reach allows you to hit multiple enemies deep with a single swing. This means if you have a zombie behind a zombie and hit the front zombie with a Katana at very close range, you'll also hit the zombie behind the front zombie, in addition to any zombies to the immediate left and right of the front zombie.
Large arcs and furthest reach;
- Katana
- Guitar
- Axe
- Golf Club
- Baseball/Cricket Bat
The remaining melee weapons are all shorter range with smaller arcs;
- Crowbar
- Frying Pan
- Nightstick
- Machete
- Chainsaw
As discussed in the other answer the damage per hit of each weapon is the same, with the exception of the chainsaw. The main difference between the weapons is attack speed, which is detailed in the other answer as well.
Best Answer
The Gong Show achievement is also affected by your health; if you are low on health you will not unlock the achievement. So it seems reasonable to assume that the mini-game simply checks for health and adrenaline, without having to conclude that adrenaline actually affects melee damage per hit.