I've traded on both, and there are positives & negatives to both.

Bittrex
(+) More established reputation (although individual experience varies)
(+) Typically more liquidity for big coins (usually not a factor for most)
(+) Exclusives (Cardano used to be only available here, not true anymore)
(-) High commissions (more than double compared to Binance at the moment)
(-) Withdrawal fees overall higher in my experience
(-) Charts need help
(+/-) Lacking many of the smaller coins. Positive and negative. Positive in the sense that it weeds out the projects that are not invested enough or large enough to get listed. Negative in the sense that there are lots of good projects that just don't want to spend the capital to get listed.
(+/-) US based

Binance
(+) Lower commissions
(+) Wide selection of alt-coins, including many smaller projects.
(+) Big community engagement: giveaways, airdrops, competitions, community choice awards
(+) Responsive support staff
(+) ZERO withdrawal fee for NEO (no accidental destruction of 0.975 NEO if you type in a whole #)
(+) Gaining popularity & trading volume is increasing
(-) Slightly new exchange, untested reputation long term
(-) Still lacks some popular coins (like NEM)
(-) Color scheme of the basic interface makes my eyes bleed
(+/-) China based

Overall, my preference right now is Binance. I've shifted most of my trading away from Bittrex mostly due to high fees. I personally did not have any issues trading on, or withdrawal from, Bittrex and it did everything I wanted from the exchange otherwise.