It totally depends on what kind of game you aim to make.
Game maker : Free, 2D
It CAN do 3D, but it's probably not the best idea. I suppose it's okayish if you aim for something simple, though.
It's more powerful than you can imagine at first, yet it does have limitations. Very useful to make game jams, prototypes and such, but can also do impressive games as well, it just needs more time.
The paid version add HTML5/iOS/Android/etc support, which isn't that expensive if you plan to make money out of your game. Good point is, Game maker fully support all versions within a single project; you don't have to code differently each version and you can export any kind at any time.
Unity3D : Free, 3D (duh)
While it can do 2D, and I think there's a decent support from the community, as its name implies it's best used for 3D.
I used this in school for my final project, I was amazed at how easy it was to use. I mean, back then they had a 3D plateformer tutorial, and in an afternoon you'd have a working 3D action game from the Playstation/N64 era.
The free version has limitations (I remember we had to make the school buy it so we could use the render to texture ahah), and I thiiiiiiiiiink I remember they also support non-PC plateforms but I don't know how/for what price (if any)/etc.
All in all, as I make mostly 2D pixel art games as a hobby, my choice go to Game Maker. I mean, sure, I don't make ultra fancy technical stuff, but in the last 4 months, with 4+ projects (mostly game jams) there isn't a single thing I wasn't able to do. And code clearly isn't my strength here ahah
Also, while I can't say I tried, I'm highly doubting that Game maker doesn't support multiple screen resolution. I know you can change resolution on the fly (that's actually how I make my games zoomed x2), and considering they're making everything possible for you to develop on Android/iOS, I can't begin to imagine why they would have fixed resolution since every phone around has a different one.
Maybe you found old information or something? (or maybe it's true, eh, I'm not pretending to know)
IMO, it's not a matter that GameMaker doesn't have enough features to make a complete game, it's just a matter of knowing how to approach a goal with code.
That is very true.

Game Maker and Unity3D have been around for a long time, which means they have tons of community support. Forum posts, videos, tutorials, there are plenty of stuff to learn.
So if you struggle with something, chances are someone already found a solution, and if not you'll find people willing to help.
A piece of advice (both from personal and professional experience): Avoid coding it from scratch. Unless you have a very specific and technical feature that can't be done overwise, work with an existing engine.
Some people might make comments such as "pfff, if you didn't made it from scratch, it's not a -real- game" or "you're not a -real- game developer". Never listen to those people. 99.9% of the time they never finish their projects. Just make your game, and finish it, that's pretty much all that matters.
Using an existing engine, with a strong community and support, will help you keep your motivation stay high, and will allow you to concentrate on the "cool" stuff your game needs, not the super boring stuff that you don't want to make and that will make you hate your project. I have a coworker who's been working on his engine for more than 7 years. He still didn't make a single working game with it.

Also, keep in mind that games such as Super Crate Box, Spelunky (original), Hotline Miami or Nuclear Throne are all made using Game maker.
Final thoughts:
Honestly, I suppose you have a specific project in mind, something you put alot of love and work in, right?
Then pick an engine or whatever, and make -something else-. Do a very small game (in a genre close to your game), learn a few tricks and make yourself comfortable so that whenever you start your game, you don't have to change engine/software afterward. It's a motivation killer.
So yeah! Pick Unity3D, Game Maker, Construct or whatever, and make something small! Maybe join a game jam (added motivation always help!) or something, and no pressure, your only goal would be to learn and make yourself at home. Maybe you'll decide that the engine you choose isn't the one you'll use in the end, but eh, it's still experience.