Logo

I'll make it simple for you
Illustrator is working with VECTOR in most of the times.
Photoshop is RASTER in most of the time, so If you're not going to retouch any picture and you just going to make some clear logo I'll recommend going with Illustrator, Yes you can do it in Photoshop but you know :D Photoshop is most likely designed to retouches etc not logo making program :D

For me I'll combine these 2 programs I would make some great logo in Illustrator and then finish it in Photoshop by adding some final touches like color correction etc.

Coming from a person who has been working basically soully in Photoshop compared to Illustrator.
I *love* the way Illustrator does pathing. It's clean, will allow me to export it to C4D without issue, and just generally looks nice.
That being said. I use Photoshop primarily. Photoshop's pixels are a little restricting when coming to editing in the future, however, it's really easy to change it regardless.
Photoshop all the way.

Photoshop is a bitmap software (used to create jpeg's, png's and so on)

Illiustrator ir Vector based software (vectors are scale-able , because everything is made out of lines and basic shapes)

Photoshop is a great program for modifying already created images or graphics, like photos, and is Adobe's most popular program whereas Illustrator is an advanced vector-based software. So, unlike Photoshop's pixel-based format, it uses mathematical constructs to create vector graphics.
Illustrator is used often to create logos or anything that may need to be printed or displayed at different sizes.

for logo you want illustrator, you want your logo to be a vector file so it can be resized to any standard. In photoshop you are not creating in vector but in bitmap instead wich will lose quality when you use in various formats.

Im a professional graphic designer, and from my expertise. I recommend making a logo on Illustrator, you want to keep your options open to printing, digital increasing the size and so on, Illustrator keeps your graphics in Vector which means they never lose quality or resolution. Look into illustrator for logos.

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