Oldschool RuneScape ironman: Motherlode Mine vs powermining

Powermining will be faster, especially if you don't have a dragon pickaxe. If you do have a dragon pickaxe, the difference isn't too big. The results aren't sensitive to moderate increases in your potential hourly income.

Method

One way to arrive at an answer is to decide, level by level, whether powermining or the Motherlode Mine will be better. (In other words, are the extra ores obtained at the Motherlode Mine worth the time spent mining?) Armed with this information, we can easily reach one of three conclusions: powermining is better at every level, the Motherlode Mine is better at every level, or each method is better at specific levels.

For each Mining level, we want to know if the ores we receive from the Motherlode Mine compensate for the extra time spent mining (compared to powermining). To figure this out, we need to know:

• the Mining experience per hour for each method;
• the ores per hour we'll receive if we go to the Motherlode Mine (MLM);
• the Smithing exp we'll get from these ores;
• and how long it would take to get this Smithing exp with no MLM ores

This way, we can figure out how much longer each Mining level takes at MLM, and how much Smithing training the MLM mining will save us, compared to if we'd powermined instead. If the amount of time saved training Smithing is greater than the extra time spent mining, it's better to spend the level at MLM; otherwise, it's better to powermine for the level.

Conclusion

To compute the time required for 70-90 Mining and Smithing with each method and each type of pickaxe, I used an R script implementing the method discussed above on data obtained from the sources listed in the next section, interpolating when the data did not have level-by-level granularity.

With a dragon pickaxe, powermining is faster, with 70-90 Mining and Smithing taking a combined 166 hours, compared to the 186 it would take with the Motherlode Mine method.

With a rune pickaxe, powermining is still faster, and the gap widens: now, powermining will take 172 hours, compared to the 204 of Motherlode Mine.

These results won't change with higher potential income per hour unless you can earn well over 350K gold hourly. The two Smithing training methods I consider are making mithril/adamant platebodies (slower but profitable) and smelting gold (faster but very expensive). Since making platebodies profits and is decent experience, it makes sense to fund gold smelting this way, rather than with some non-Smithing moneymaking method, unless the alternative method is far superior to the 120K per hour proposed in the OP.

Sources

Hourly experience rates for Motherlode Mine, iron powermining, and granite powermining: Motherlode Mine & XP Rates!

MLM ores from level 70 to 80: Loot from 70 - 80 Mining at MLM

MLM ores from level 67 to 70: Loot From 2000 pay dirt at motherlode mine 67-70 mining

MLM ores at level 91: 1h of MLM - 43k Mining Xp/308k GP Per Hour

Mithril platebody smithing XP rate and financials: OSRS Ironman - Smithing Guide (see description)

Dragon pickaxe comparison to rune pickaxe: Dragon Pickaxe - 2007scape Wiki - Wikia

I think in general, it's going to be better to powermine, then do moneymaking and purchasing.
It's tough to answer, as it's pretty highly dependent on how much money you can make. The best way is for you to do some tests. RuneScoop used to have a good explanation of this, but that site is defunct now.
The test I would run us:
1. Do several runs at your mining resource location (I don't know what Motherlode Mine is), probably 10-20 loads. Record mining exp gained, as well as time taken.
2. Smith all resources from #1. Again, record smithing exp gained as well as time.
3. Powermine for same amount of mining exp as #1. Record time.
4. Calculate how much you need to buy for same amount of smithing exp as #2. Go out and make that money, record how much time to make that money.
5. Smith purchased items to match exp from #2. Record time.

This way, Steps 1-2 will give the same amount of exp as steps 3-5. See which set of steps take less time, that's your winner. I think this math checks out. It'll take a bit of work, but it'll give you the best answer.

I don't think dragon pickaxe or your goal levels will affect the result, since it's the same in both scenarios.