I picked Gibson SG over Fender Strat. I currently own a SG special "faded" and a SG standard. I used to have a Squire Strat, loved the way the body of the guitar felt but being the bottom end of the Fender line the electronics and workmanship left ALOT to be desired. However the American Standard was very sweet.
I will eventually own a Strat of some sort, but for now I'm happy with my choice in the Gibsons.
Reasons I chose the SG over the Strat.
Sound.
The SG sounds really very nice with the stock pick-ups but those can easily be changed on any guitar. The body resonates, from the tip of the neck all the way through the body. The set neck offers a sustain level thats unparalelled by bolt on neck designs. To me it just has a better, sweeter sound than the Strat.
Playability.
The Strat is heavier. The SG is so light and comfortable to strap on. It makes it much more fun when your comfortable and can play as long as you want without any discomfort. The one big disadvantage is the SG tends to be neck heavy. It takes a bit to get used to it and requires a decent strap, preferably leather, that will stay in position better because it kind of clings to your shirt.
The frets are fairly high on the SG and combined with a 12" radius fret board makes bending really easy and precise.
The medium scale length makes it easier for me to reach frets and the wide, meaty neck fits my hand better than the Strat.
Now it's a given that SG's are prone to having the neck break it they are dropped or mishandled. This is because the headstock bends 17 degrees and Gibson crafts the necks out of a solid hunk of wood, rather than a thinner slab of maple like a Strat. But given proper care there shouldn't be any problem, it's not going to just pop off one day out of the blue.
As for the tuning issues, I haven't had any with either of my SG's. I don't know how long a guitar should stay in tune, but as long as the weather/humidity has been consistant I never have to retune from day to day. I have an amp with built in tuner so I check tune each time I plug it in and it's rare that I need to do more than a minor adjustment on one or two strings.
Fit and finish/quality
I'd hesitate to say Fender or Gibson is better than the other. Fender has an advantage that their guitars are more or less "modular" since they are two seperate pieces. The body and the neck. Both finished seperately and indipendant of one another. So if one piece is substandard it's much easier to swap out. Once a neck is set and glued in, it would require alot of work to remove either part on a Gibson. Also Gibsons require alot more hand crafting. Actual people sanding and finishing the bodies and necks, not machines. Thats part of the reason they can be pricey and why you can find some quality issues on some Gibsons that may not be as comon on a Fender.
For what it's worth, playing blues (my personal favorite music to play) on a Gibson is absolutely possible and sounds fantastic. You can't always go by what artists are playing, they get their guitars for free. There is also the ability to coil tap humbuckers to get a single coil tone, if thats your thing. And you can buy Strats with Humbuckers. So thats more of a personal taste. There are a pleathora of pick up variants out there that you can swap out and fit to any guitar.
In my opinion you really need to play them and see which is better for your personal tastes. I also really like the classic good looks of the SG and the Strat. Both are classics. I'm not a huge fan of the Les Paul style bodies, they are beautiful guitars but look too upscale for me.
By the way, most of my favorite guitarists play(ed) Strats, or Strat style guitars. But there's just something about a gibson SG.