I've used LA's Totally Awesome All Purpose Degreaser (dollartree.com; yes, I buy it by the case...lol. Not just for the car, but granted, the car does get a lot of it) to manually clean around the dirty parts.
And I will just say this, it's soooo much easier working on a clean engine bay
If you want to really get your clean on, get some ramps, and put the vehicle on ramps and get the undercarriage
As with any "Degreaser" you gotta be careful, don't let the solution sit for a long period (or worse, dry out/evaporate...) on the aluminum parts, as some of these commercial "Degreasers" are known to cause etching/corrosion on metal parts.
If I recall, Simple Green was the "most popular" among that category.
I can't see much harm in soaking under the hood, my local car wash actually has an "Engine Degreaser" option on their self-serve stations, it brings the hose pressure down to a near "trickle", to dribble around the real dirty areas, then let it soak a little bit (go ahead and clean the wheels and rims), then come back and hose off the degreaser with the rinse.
Just stay away from the "spot free rinse" - a friend of mine does this car wash engine degreaser about every 6 months, and he said the one time he used the "spot free rinse" it left a strange "film" all under the hood.....almost like a wax...