I'm no expert, but I think Dr. Mario is fantastic. A testament to why I main him. XD
He's definitely far from a "bad Mario" in my eyes. I think the main difference between the two is that while Mario has an easier time getting off combos due to his higher speed, Dr. Mario's successful combos are more potent to his increased power. Heck, I don't feel that Dr. Mario even needs many combos. His attacks are powerful enough that reads and punishes alone are quick and easy ways to get a stock taken.
Most people who think of him as bad usually cite his recovery, which is undoubtedly worse compared to Mario's, since he has lower jump height and I believe that his Super Jump Punch has a bit less vertical height than Mario's. His Super Sheet also doesn't cause Dr. Mario to float for a bit unlike Mario's Cape, which is a huge problem considering every other factor. On the plus side, he has the Dr. Tornado to help aid his recovery!
Detractors also sometimes talk about the arc of his Megavitamins. Because of the way they bounce, they can bounce over extremely small characters like Kirby and Jigglypuff, unlike Mario's Fireball. Personally, this is kind of a moot point to me. Problems with their arc can easily be averted by using them midair. They're also physical projectiles, which is IMO, a great selling point for them. They can't be absorbed by Ness, Lucas, and Mr. Game & Watch for free health or dangerous attacks.
Another difference that I see brought up often is their forward airs. Lots of people think Mario's forward air is better because it's a meteor smash, and dismiss Dr. Mario's since it's just an attack that launches. I feel that this is also a moot point, since Dr. Mario's forward air will be strong enough to KO past the horizontal blast lines (or make them fly far enough to the point they can't recover) at the same percentages that Mario would successfully meteor smash. Dr. Mario's offstage forward air can KO most characters at around 60%-80%, if I'm not mistaken... that's pretty major.
...I feel like I'm kind of lost in what exactly what I was trying to say with this post, and also dragging it on. XD I guess debunking reasons why people think Dr. Mario is worse than Mario? But, anyway, you'd be right in saying that he's considered worse than Mario due to his offstage ability, among other things. I feel, however, in the hands of an experienced user who can bring out his strengths, like Boss, he's not explicitly worse than Mario, just a lot different.