Which is better for running?

The Avia 5000. It is built as a neutral running shoe with foam cushioning and an 11.2 mm heel drop. The Skechers Geno is a casual slip-on, not a running shoe.

Which is better for wide feet?

The Skechers Geno, which comes in wide width. The Avia 5000 is listed in medium width only, so wide-footed runners should look elsewhere.

Hard to say from specs alone. The Avia has a thermoplastic rubber outsole and a much larger pool of owner feedback; the Skechers has few ratings so far. Neither carries a written warranty.

Is the Skechers Geno worth stepping up to over the Avia?

Only if slip-on convenience, a memory foam insole or a wide fit matter more to you than running capability. For exercise, the Avia is the more capable shoe.

Can I wear the Avia 5000 all day?

Yes, but it is a running shoe with a thick heel and low arch support. The Skechers slip-on is the easier all-day choice for standing and errands.

Do either have arch support for flat feet?

The Avia lists low arch support, which suits flatter feet. The Skechers does not publish arch support details, so try it on if you need firm support.

Avia Men's 5000 Running Sneakers vs Skechers Geno Slip-On Sneaker

Buy the Avia 5000 if you actually run or walk for exercise and want a neutral running shoe with real cushioning. Buy the Skechers Geno if you want a slip-on for all-day standing and errands, especially in a wide fit. The Avia has far more owner feedback behind it, but the Skechers has the better-known comfort insole and a vegan build.

Choose the Avia 5000 if you want a lace-up neutral running shoe for walking, jogging and gym days.
Choose the Skechers Geno if you want a slip-on wide-fit sneaker for standing, travel and everyday wear.

Prices

Avia Men's 5000 Running Sneakers: $8.00 at Vijay Shanthi Builders (checked today)
Skechers Geno Slip-On Sneaker: $40.00 at Walmart (checked today)
Difference: the Avia Men's 5000 Running Sneakers is $32.00 cheaper than the Skechers Geno Slip-On Sneaker today