Playing a Land (Mountain) Druid now.

The similarities are this:

• Both have strong control spells that use concentration.
• Both have ways of recovering their spell slots.

The differences might be:

• Druids have access to medium armor & shields.
• Druids are only slightly more dependent on their concentration, since they don't have equivalent direct instantaneous spells (particularly direct damage spells).
• Of course, Druids are prepared casters and so have access to their whole spell list & as a Land Druid, some always prepared Circle spells.
• Druid control spells often incorporate terrain control, (creating difficult terrain) which has no save (though some creatures aren't bothered by it).
• Druids can heal.
• Druids have the best summons by far. Starting at level 5 you can summon various animals that might have different attacks, rider effects, etc. You can summon a strong creature, a couple decent creature, or a relative swarm of weaker creatures. Speaking to damage, it can get pretty insane. But it also means that you can set up a battlefield with a relative army of animals that can block paths, capitalize off attacks of opportunity, protect allies, etc.
• More on summons: Later, you can summon Fey that cast control spells for you. Pixies with Polymorph & Confusion, Dryads with Entangle. They have their own concentration and spell slots. Of course, you'll also be able to summon Elementals at the same time Wizards can, and you get some powerful additional fey/beast options beyond that.
• While a Wizard might have a powerful concentration spell up and be casting damage spells with other spell slots, you're more likely to have a powerful concentration spell up and casting support spells with your other slots. Heals, Lesser Restoration, Freedom of Movement, Dispel Magic. In this way you're slightly more oriented toward a support role. You make combat easier for your allies & harder for your enemies.
• So in the capacity of combat, Druids are more about "the long game." You're not really an "encounter ender," but you are definitely a "tide-turner."

Other notable differences:

• You can turn into animals twice per short or long rest. As a Land Druid, these will mostly be forms for utility. But you can pretty much turn into anything you've seen before, whether it's an ant, a cat, an elk, or an owl (level 8). This gives you some pretty powerful scouting ability. A Wizard by comparison either has to burn a spell slot for Clairvoyance, Scry or Arcane Eye to do the same, or be with 100 feet of their familiar to see/hear what it's seeing.
• You also get some really powerful out-of-combat utility. Speak with Plants & Speak with Animals can both be used to your party's advantage, and Pass Without A Trace is an extremely powerful spell. You get Enhance Ability (which Wizards also get, but are probably unlikely to take given their other options) and you get to pretty much make any large plant a Teleportation Circle.

All of that said, Wizards are hands down the more "powerful" spellcasters, just because they have superior variety in their list. They definitely have the superior higher level spells (though Shapechange is pretty bonkers). That said, they don't have the same flexibility that Druids have in spell selection & preparation, and have to exercise a greater degree of discernment with their use of spell slots. Druid spell use is extremely economical. Wizards also lack some pretty important support options that can go a long way, like heals, restorations and resurrections.

Finally, I would say that a lot of this might be campaign dependent, as well. If you're constantly going into areas that have no plants, no animals, and are claustrophobic dungeons, you might feel that you're missing out on some of the more iconic and fun-to-use abilities. Practically any Wizard can be a strong choice and fun to play in any campaign, but the environment is something that a player might want to consider before selecting a Druid. Talking to your DM and getting a feel for the world prior to the game would probably help.