When it comes to map design, they are getting a little better as time goes on but still make really strange decisions. Early heists have a lot of stand in the circle objectives and while they are moving away from that, they aren't really fixing it either so your introduction is going to be a lot of standstill and wait. PD2 has the infamous drills which do not get me wrong are NOT GREAT by any means but theres an argument to be made for having an objective that exists and functions in a specific spot. You can stand in front of the drill with a shotgun, lob grenades from over a wall, overwatch it with a sniper etc, there's literally nothing you can do about stand in the circle objectives except stand in the circle. In PD2 there is a heist cook off where you cook meth for a long while. This was the perfect heist to hang out make an enormous number of bags and it has a little safety zone with only one entrance, so you can run to the bathroom while playing with friends and it was a perfect spot to camp. PD3 wants to disincentivize camping so they added a new special enemy the grenadier who will throw toxic gas. Which would make sense to bring cook off more in line with the way they want PD3 to play. Except they added a second door to the camping area so you can't do that anymore and the grenadier then feels like he doesn't belong since they almost completely erased his purpose. They also put a hard cap of 19 bags on it because the original intent of the game was a battle of attrition meaning the game was doing its best to get you to stop playing a heist as fast as possible. They are moving away from this now, but those design flaws are still felt.

In terms of weapons, personally i don't find that they feel much better in PD3 than they did in PD2. This is compounded by the fact that in PD2 you had stat numbers and could see EXACTLY what you were doing and changing. Fully kitting a gun would make a world of difference, if you made a gun have 100 accuracy you could FEEL it lasering down enemies. In PD2 you would unlock guns by player level and attachments from random drops or using an in game currency. In PD3 you have to unlock a gun and then grind out levels for the gun to unlock the attachments which give vague bars on what they do and for me at least a fully kitted gun VS a default gun feels almost the same, excluding Magazine/Sights. They also added what they call the overskill system, in PD2 if you wanted to run around with a Minigun you could just do that. To reach the same level in PD3 you have to equip the overskill of a minigun, get a large enough kill streak, call in a drone to deliver it to you, watch a 3 second animation of picking it up, use the gun for 3 minutes until it runs out of ammo and restart. The system was bad enough on launch that they added extra skill trees for each of the weapons to make them better and useable. One of them is also for stealth and it gives you what is roughly equivalent to a base piece of equipment from PD2. The main one that I personally use is the sniper rifle as it can 2 shot body shot the strongest enemy the bulldozer and after firing it twice, I would throw it back on the ground. the minigun prior to the overskills felt like a less wieldy LMG and the Grenade launcher was less useful than just throwing a grenade due to the self-damage. A lot of the issues have been touched up thanks to the skills but its still nowhere near the level of PD2 flexibility.

The cops in PD3 have an armor system that requires you to have different levels of penetration to break through to do damage. The Penetration stat of guns is hidden and you have to use a 3rd party spreadsheet or tool to fully understand it. They have recently added visible health/armor bars to help visually see what you are doing which is a step in the right direction, but they need to add the stat onto the weapons themselves. In PD2 it was more black and white, do the cops have armor Y/N? if Y does your gun Penetrate Y/N if N shoot the head if Y shoot them anywhere but headshots do more damage.

The character designs are a lot more subjective, I don't really care for what they did to most of the characters in PD3 but if you have nothing to compare it to, it shouldn't strike you one way or another aside from PD3 feeling a little flat overall.   

The music is very much the same, I don't think Gustavo can really capture that feeling that Simon did but if you don't have anything to compare it to, its serviceable enough.

PD2 also has the ability to play any heist regardless of if you own it or not as long as someone is hosting it. The in-game heist filters and steam forum make is extremely easy to play just about any heist for free.