I'm going to be running a Harry Potter game in the near future, and I don't really know what system would be best for the kind of game that I want to run. The vast majority of my experience is in D&D of various stripes, with a dash of GURPS and some homebrew systems for flavour.
Unfortunately, there really isn't a D&D system (that I know of) that ports well into a Harry Potter game. The spell system in Harry Potter has a lot of stuff in it that doesn't really work well with D&D's spell system, and if a system requires that I rewrite giant pieces of it in order to make my game work, I'd rather find a new system.
Here are the salient features of the game:
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The Harry Potter setting. This means that the system should be able to handle magical creatures, various forms of spellcasting, as well as modern technology in the same system.
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The Harry Potter spell system. Spells shouldn't be a strictly limited resource, it should be hard or impossible to resist a spell once it hits you (for the most part), and learning new spells should be easy, but not necessarily trivial. I don't necessarily need to have the spell list from Harry Potter already made for me, but creating individual spells as a GM should be easy to do, so I can make up a few dozen for my players to choose from at the start without spending tons of time on it.
I'm not really leaning towards any specific kind of spellmaking system. If it's a GURPS-style system, where you build a spell based on its effects and all spells need to be built beforehand, that works for me. If it's based on magic words that mimic the faux-latin of the books that can be combined on the fly, that works too. As long as the system is robust enough to let me make most or all of the spells from the books eventually, and each spell doesn't take a ton of time to make.
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No huge magic/martial gap. I'm used to D&D, where your optimal option was to be a full caster, and anything else was going to end up worse barring some serious munchkining. I'd like a system that doesn't say "magic will solve all of your problems", and that makes non-magical action just as good in its own way.
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A dark tone. The players will be wizards (or sentient magical creatures) that never went to Hogwarts, and are both politically and economically disadvantaged. Characters should be able to die and have bad things happen to them, and the system shouldn't assume any zaniness. In addition, this criteria makes most direct Harry Potter systems non-viable; all the ones I'm aware of have significant investment in the house system and Hogwarts, where this is a campaign about adults who never went there.
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An ideal system should contain robust systems for stealth, espionage in general, combat, social interactions, and a basic system to handle player wealth.
In general, I'd prefer a system that's more narrative that simulationist, though that's not a hard criteria. I'm looking for a system that will help me tell a story in the Harry Potter world, and not one that will help me simulate the world and have the cards fall where they may.
Best Answer
My recommended system for a Harry Potter game would be Savage Worlds.
The Harry Potter setting
There are numerous existing settings that successfully mix magic and technology e.g. Agents of Oblivion, and stats for a large number of standard magical creatures existing in published and free supplements such as The Savage Worlds Beastiary. There are also guidelines for creating your own playable races included in the core rulebook.
The Harry Potter spell system
Savage Worlds supports a wide variety of approaches to spell casting and the core rulebook has a number of arcane backgrounds as examples. Other supplements e.g. Hellfrost, provide examples of how you might approach things like the potion making that forms a large part of the Harry Potter universe.
One of the possibilities outlined is to use a 'no power point system'. This means that spells are not tied to a particular resource. New spells are typically tied to buying Edges, which you can do with character advances that are earned from gaining experience. Other approaches also give free spells when you gain certain levels of experience. New spells are generally relatively straightforward to design, and there are many, many examples of other peoples' efforts on the official forums.
No huge magic/martial gap
There is a relatively small school of thought that this is an issue with Savage Worlds, but most disagree. The fact that you will be designing your spells yourself means that you should be able to ensure that martial and magical approaches are balanced to your satisfaction, but most would say that this is also true with the core set of rules.
A dark tone
Savage Worlds can be dark and dangerous, with Bennies offering one of the main ways of affecting this. These are similar to things like Fate Points and allow you to try to avoid taking damage, reroll failed rolls etc. You can certainly die in the system and have bad things happen to you, and there optional setting rules that can tweak the danger even further.
An ideal system should contain robust systems for stealth, espionage in general, combat, social interactions, and a basic system to handle player wealth.
There are basic skills for stealth, social interaction and combat, and published settings where espionage is a greater focus such as Deadlands Noir have extended rules to cover this as well. Social Conflicts and Dramatic Tasks offer a greater level of challenge for extended and more complex tasks for players, and there is a basic economic system built into Savage Worlds that is easy to tweak to your needs.
Conclusions
This has been attempted before using Savage Worlds. One of the most notable conversions includes input from the Savage Worlds official brand manager Clint Black, and the pdf can be found here. It is a completed setting, and you should definitely take a look at it as it might save you a lot of work.
There have also been other similar efforts such as here, and here.
I have personally run several games with settings that similar to Harry Potter in different ways, and that meet the individual requirements you specify in your question with a great deal of success. Most notable was a modern setting that mixed magic and technology, making use of the no power points rule. This was successful, enjoyed by players and myself, and for this reason I believe Savage Worlds is ideal for a Harry Potter universe using the criteria you specify. You could easily pick and choose elements from existing published settings to form a lot of the required design. It is typically described as rules-efficient rather than rules light, and I would say it leans towards being narrative driven.
The official forums are generally extremely supportive to people designing homebrew settings, so any questions you have whilst doing this would be helpfully and quickly answered.
There is also an existing setting which is based on the premise of students going through a college in America where weird and wonderful things happen (East Texas University), so this type of setting has been proved to work with Savage Worlds.
Useful links: