If you haven't already read Brian's blog post about how this started, you should do that, and then come back.
Initially I thought Aspects would be an impossible companion to Gumshoe, like suggesting that onions go well with caramel. But after some thoughts (which I'll outline), Aspects fit very easily into Gumshoe, if you're willing to hack Gumshoe a little and make it less about dice or points and more about what-all you need to do to tell the most complete, compelling and investigative story possible.
Aspects are "narrative mechanics" (my term), meaning they allow the story to be told by the player and act as codified rules - the world of the story is influenced by and operates under their consequences (that's a Fate pun!). Aspects imply and inform on skills - you have an aspect that reinforces or qualifies a skill to help shape the character. This is Fate's strength.
Gumshoe is already a narrative system, though one that prizes investigation and skill application over the act of storytelling and collaborative narration. Whereas Fate loosens the reins on how the story goes forward, leaving it up to the player to bridge the gap between skills (which are loosely named) and application, Gumshoe very regularly applies targeted skills (Evidence Collection, Bullshit Detector, Reassurance, etc) that may get either broad or specific use by players.
Where Gumshoe opens the door is through application of Drive and Nationality...those two backstory components that influence what brought the character to the point wherein we "meet" them on the character sheet. How a player determines these elements is similar to how a player determines Aspects...and it is there that we see the mounting point for Aspects on a larger scale.
Going forward, I'm going to make some assumptions here:
1. You've got some Gumshoe and Fate knowledge, either playing or running or both.
2. You're granting me some leeway to let this discussion persist.
3. You've got an end goal of telling the best story/game possible, not the ultimate elevation of one system over another for the sake of business or pride or something.
If you replace Nationality/Drive with an Aspect pool, Aspects fit in quite nicely with Gumshoe. There are already point-pools present and point-spending is not a foreign concept to a Gumshoe player. Here we are simply granting additional pools upon which to draw from.
Whereas Brian gave the Fate flavors, I will give the non-Fate flavors here:
A. The Investigative -- This pool augments Investigative or General Abilities because it describes a person's nature in the realm of investigation. This is also called a "Curiousity", if you're looking to keep things on par with High Concept and Trouble. "How does my character view the unknown?" is the question here.
B. The Combative -- This pool is more for General Abilities but the Interpersonal skills could work here as well, and applies to situations where between two parties the possible outcomes involve knuckle sandwiches and shootouts. If you're looking for a single-word title, call this pool the "Fuse", and it answers the question, "When does my character throw down? In what situations?"
C. The Intimate -- Again this pool is Interpersonal, but also General or even a little Technical depending on context. This pool answers the question, "How does my character handle things between him/herself and other players?"
Examples of Aspects based on these questions:
A. "The unknown is an invitation to gain power."
B. "Fighting is the method of idiots"
C. "People are made to be stepped on."
And just like that, I wrote a cult leading villain.
As Brian suggested, offering refresh is the economy of choice here. As to how many points sit in pools A, B, C, I would suggest no more than 5 apiece to get started, but that is entirely a fluid number. I tested it with 5 apiece (meaning I augmented the standard build in Night's Black Agents with 15 additional points), but I'm toying with the idea of having 10 points spread across 3 categories.
These Aspect pools don't trigger refresh by themselves, the story must move narratively and forward to warrant refresh. This is not a case of spend from the Aspect, refresh the Skill, spend Skill, refresh from Aspect ad nauseum, these are designed as possible bridges to granted characters the flexibility of Aspects of their own design under the banner of a skill-oriented Gumshoe experience.
By no means is this idea complete or finalized, these are just the thoughts I've had today and written down here for the curious. I'll revisit this idea more in-depth as time permits.