They were both comic relief. The Doctor was better because his character was a deeper, more developed character that viewers cared more about, so the humorous situations he was placed in had more depth and situational resonance.
Neelix was a sight-gag first and a character second. For an actor, that’s a lot to work around. Certainly, Phillips was the guy for the job, and he had his spotlight moments in the series, but he was only really an endearing character sometimes and mostly at the end of VOY’s run. How his character was painted in the first three seasons made it really hard to like him at all. The writers eventually did his character right, but he’ll never be as beloved as other characters, especially the Doctor.
Edit: Phillips, on the other hand, has earned his place as ST royalty.
I really agree. Neelix’s obnoxious behavior and strange jealousy / possessiveness of Kes was a real disservice to his character for the first few seasons and initially I couldn’t stand him. He improved a lot once he and Kes broke up. It was an uncomfortable relationship to watch anyway because Kes was maybe the equivalent of a very sheltered, naive 18-year-old human, and Neelix was clearly a middle-aged dude who had been around the block a few times. He was half controlling parent, half controlling boyfriend and it was just weird.
He became such a wonderful, warm person as the series went on. Godfather to Naomi, took his jobs as chef and morale officer seriously (even though everyone ungratefully complained about his cooking!), trained as a security officer, and always a friendly ear to anyone who needed him.
I’ll also make this argument in his favor: Neelix didn’t have much of an ego, whereas the Doctor was unbearable at times. Neelix’s EQ was much higher.
I think you can explain most of Neelix’s behavior in the first few seasons on severe PTSD considering what happened to him before he went on the run.
For many people Neelix is a write off because of just how gross his relationship with Kes is. It’s a shame too, his introduction to the series is 100% wildcard. I was most excited about his character when I watched the first time. And then all my excitement was spoiled by constant couch talk about how Neelix is just a gross pedophile.
Some real whacky choices were made with voy.
This, exactly. Neelix was a pretty unmoored character in a show where each character’s development relied heavily upon interplay on a counterpart. Neelix only had Kes to rely on, but Kes was the Doctor’s counterpart. Mostly, which left Neelix not much to play on, but the jealousy for the first part of the series. It resulted just as you described, poorly.
Once Seven was introduced, and a bunch of other characters could connect to her, and then Neelix could connect to both Naomi and to Seven, everything really fell into place for both Neelix, and for a bunch of other characters. 
Kes was a real drag on the show for so very many reasons. I was so glad when they got rid of her character. 
