I was a consultant at Bain, so I certainly know the consulting side of the story. I also have friends at Facebook and Google, so even though I don't have direct experience from these companies, I can tell you what I feel is the case.
In general, I think it's more stressful at the McK, BCG and Bain because:
1. You work for a client. The client has paid a lot for your services, your project has a deadline, and the client is determined to extract as much value from you in the given timeframe.
2. You are rarely an expert at the start of whatever project you are working on, so the learning curve is very steep in each project. You often feel like an impostor if you are working in a highly specific area (say, avionics systems) for people with 25 years of experience. The ever-lasting newness can be exhilarating at the beginning, but it can wear you down with time.
3. Projects are often of a stressful nature - transformation, cost-cutting, due dilligence. At major tech companies you often work on more organic things.
On the other hand, it can sometimes be stressful at Google and Facebook because:
1. In some departments, especially sales, you have very strict targets (e.g. monthly sales), so it's stressful if you are not on track to meet those
2. You work with the same people constantly, which can be a double-edged sword. If your boss/colleague is generating stress, you are less likely than in consulting to break free from them in the short term
Hope it's helpful!