Yes, one time frame is as good as another. It's all your personal preference as to how fast you want the action to be. When trading moving averages, you look to make a profit from the middle of the up swing and down swing. The smaller the time frame, the smaller those middles will be. Of course I don't use MAs anymore because I don't like the tradeoff between group delay (i.e. lag) and attenuation ability. I trade cycles.
I posted the same image in another thread where proftradingjourney was wondering where the edge comes from for a purely technical Forex trader. There, I wrote that it seems to me that if a technical trader simply buys when an asset is rising and sells when it's falling, that's all the edge they need. On the chart below, generally speaking, the asset is assumed to be rising if the green moving average is sloping upward, or falling if the green moving average is sloping downward. Long positions are entered when price is rejected by the lower (blue) band of the Donchian channel, typically confirmed by candlesticks crossing above the black moving average, and doubly validated as the black moving average begins to hook upward. Conversely, short positions are entered when price bounces off the top (red) band of the Donchian channel, typically confirmed by candlesticks crossing below the black moving average, and doubly validated when the black moving average begins to hook downward. Profit can be taken when candlesticks reach the opposite side of the Donchian channel and/or when it seems the run is coming to an end, as conveyed by the black moving average turning around and heading in the opposite direction. Positions might also be entered when price pulls back behind a sharply sloping green moving average and/or behind the purple moving average when the green and purple moving averages are both sloping in the same direction.