There's a lot of variety within both of those fields. I'm an architect so my first thought is that you are speaking of the kind of engineers that work in the building industry. But I also know some mechanical engineers who design everyday consumer products and some who make super-specialized hospital equipment and such.
Most engineers seem to me to have to interact with people more than you might think. Structural engineers sit in the office and calculate and draw, but they also answer the architect's incessant questions & requests, and they have to go to the job site to work with the contractor and to inspect periodically throughout building. Mechanical engineers in the building industry (as in, the people who design the HVAC and plumbing-type stuff) also have to work with architects and contractors and visit the job site. Product design type mechanical engineers might have less people-stuff in their job, but the more design-oriented the position, the more people interaction: most things are designed by teams, not individuals, and you might have to oversee user testing and meet with the clueless clients and bosses who have no idea what it is you are really doing and the guys in the model shop, etc, etc.
Overall, a whole lot less people-oriented than most service industries, but not isolated either.