Stone Edge vs Earthquake ?

MS/SE is better for defence as it provides more coverage, while MS/EQ is better on offence like you said because they're the same type so against good matchups both will be super effective.

MS/EQ should be better on offence too because there's more types you're advantageous against. The types that rock is SE against that ground is not (ice, flying and bug), you wouldn't use a Rhydon for anyway.

Also it really grinds my gears when someone thinks a charge move is good because it deals high DPS. Your overall DPS is what matters, because you cannot only use your charge move. Because of this, charge moves that deal high DPS for longer are better than charge moves that deal the same (or slightly more) DPS over a shorter period of time, because longer moves make up a larger percentage of an overall damage cycle (your damage from quick moves and charge moves combined) and therefore mean they increase the average DPS more.

If you had a charge move that did 1 damage in 0.001s it would have 1000 DPS but it'd still be a shit charge move because it would have almost no impact on your overall DPS.

EQ and rock have advantages and disadvantages over each other. Therefore depending on the use one will be better than the other. DPS isnt the only factor. EQ is SE on rock for example...
Imo EQ has better typing overall at least for now with Gen 1. But SEdge is better against Lapras, Dragonite and Snoralax.

Having two moves of the same type is good for pokemon you use for training and attacking, but having mixed type moves provides more coverage for gym defenders.

I have two 90+ Rhydons, one with MS and SE the other with MS and EQ. Honestly, both of them kick Snorlax butt with the same efficiency. Typing weakness and preference will dictate how you use it, but in my actual combat experience I'm really not seeing much of difference.

IN THE LINES BELOW, I WILL BE TALKING ABOUT THE OFFENSIVE RHYDON ONLY!

In a simple calculus, you will see that earthquake is slightly better. Otherwise, as the cooldown of earthquake takes 4.2secs while Stone Edge takes 3.1secs, using SE allows you to recover energy faster, so you can use the charge move more times (it won't make that difference considering that a full battle normally won't take more than two cycles, maybe in the next generation agains Blissey).

--------calculus if you want to know--------
-Mud Slap
DPS w/ Stab = 13.89
Cooldown = 1.35sec

-Stone Edge
DPS w/ Stab = 32.26
Cooldown = 3.1sec

-Earthquake
DPS w/ Stab = 29.76
Cooldown = 4.2sec

Considering that EQ cooldown is the longest with 4.2 sec, we need to use at least 4.2 seconds to calculate it. I will use 5 seconds.

time = rhydon w/ EQ --- Rhydon w/ SE
1sec = 29.76 --- 32.26
2sec = 29.76 --- 32.26
3sec = 29.76 --- 32.26
4sec = 29.76 --- (32.36x0.1sec)+(13.89x0.9sec) = 15.737
5sec = (29.76x0.2sec)+(13.89x0.8sec) = 17.064 --- 13.89

TOTAL IN 5 SECS
Rhydon w/ EQ deals 136.1056
Rhydon w/ SE deals 126.397

So, if you take short battles that you only use the charge move 2 or 3 times, that are most of the battles, Earthquake will be better. If you want to use Rhydon against pokemons that are weak against Stone, go with SE. But in the first generation at least, there are two pokemon at gyms that are weak against rock: Lapras and Dragonite. You should not use Rhydon against Lapras because Ice has advantage against the ground type. So Rhydon w/ SE would mostly be a Dragonite counter. If you want to battle Dragonite, use the SE one. If you want to battle any other pokemon, go for EQ.

I, particularly, prefer EQ.

Do all the math you all want. EQ seems more useful, not worth the trouble of rerolling for a new moveset though.

In the current gen I actually prefer SE...by a pretty large margin. And I have and have used both.

People talk about having same types on both charge and quick moves...A) who cares if they're both STAB? and B) if you have a choice of the charge move's type you should choose the more effective one...not just the one that's the same as the quick move.

Talking about type coverage, ground attacks are great vs. almost nobody useful....except fire which stone is also effective against. The other 4 - Poison, Rock, Steel, and Electric,are pretty un-inspiring. Not only are they very uncommon gym defenders, but Poison and Rock are both easily dealt with using Water. There's only one steel Pokemon. That leaves Electric. If having a super effective quick move and resisting their dmg isn't enough to beat them, then I don't know what to tell you....

Stone Edge on the other hand does extra dmg to Lapras AND Dragonite AND Gyarados, all of which, as I'm sure you know, are common gym defenders. It also will be just as effective vs. Snorlax

Just my 2 cents

My opinion:
EQ is better, but Rhyhorn candies aren't exactly common and the chance of getting a good moveset on Rhydon is ultimately 1/3 (1/2 for getting the right quick move, then 2/3 for a usable charge move).

So stick with the SE one. It's really close anyways - as clearly shown by the debate here. I think it's pretty non-negotiable that EQ is stronger regardless of how people "feel", but either way it's close and SE has a small benefit in having a lower cooldown.