Great question. It is one I hear a lot and one I have pondered many times. I have used these and other ME protocols with equal success. I tend to lean toward the gym ME for runners and skimo racers. I lean toward weighted hiking (either on a stair machine, actual stairs, or a steep hill for mountaineers.
However I have mixed these using the gym ME progressions for 6-10 weeks before shifting to steep weighted hiking for mountaineers. I have used weighted stairmaster for mountain runners as well. You might recall that in a couple of podcasts I have done with Jack Kuenzle he did a LOT of stair master ME in preparation for some of his mountain running and skiing FKT.
This may not seem very helpful in answering your question but you can take some solace that you can come at this from different directions and still get very good results. With some of the athletes I have coached for years we have tried all these combos with no significant differences and we end up either going with the one that the athlete enjoys more or we cycle them at different times of the year.
The thing that is similar across all of them is that we always include ME in every athletes training.
Scott