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.
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.
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.
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