Best: Conquest, hands down.
Manages to have engaging gameplay by giving enemies skills which make them challenging to kill (such as Counter on Archers, a group of defensive enemies with particular ones having a lot of rally skills, various setups involving Lunge). The way the AI is programmed also makes killing enemies more difficult, since you can't merely lure them in one at a time. This game does especially good with making enemies challenging without relying on forged weapons. Instead, they give enemies a specific weapon that makes them more challenging to approach (such as putting a Swordcatcher enemy to prevent Xander from tanking them with Siegfried and giving an enemy with Certain Blow and Death Blow a Great Club). Asides from unit balance (which a lot of games don't seem to get correct anyways), the gameplay of Conquest is solid.
Worst: Definitely Genealogy of the Holy War. This game does many things to significantly separate good units and bad units.
The worst thing being Pursuit. Double Attacking allows one to do quite a bit more damage. If you only grant that ability to select units with a certain skill, the units who have that skill will undeniably be better. Another thing that separates them are Mounts. Not only does this game make the movement difference between foot units and mounted units higher (even if it is by one, it still makes a significant difference), it also has bigger maps to emphasize just how much better mounted units are. One last thing is Holy Blood. A unit having holy blood make their growths better, alongside giving them higher weapon ranks for certain types of weapons off the bat. This problem is only made worse by the existence of Holy Weapons, which allow certain units in a pool of units with holy blood (with Major Holy Blood being a thing) to be significantly better than most units by using a weapon that not only has an overkill amount of might but also gives a ridiculous amount of stat boosts. Another terrible thing about this game is the horrendous weapon balance. Weapon types mostly differ from each other by weight, with Anima Magic only differing by weight. This makes units who wield Swords and Wind Magic good units while it makes those who use Axes and Fire Magic disgustingly terrible. Hell, the one playable unit that is considered good with Axes has to rely on a Mount, alongside with getting an Axe from a completely cryptic event to be good. Which leads to my next argument.
Another thing that makes the gameplay bad is the inclusion of cryptic events that offer good items. In specific, you need to have a specific unit go on a specific tile of a giant map just to be able to get specific items. This wouldn't be too bad if it only gave items that didn't make much of a difference but considering that a Brave Axe and a Pursuit Ring are on the line, this is just unacceptable. The fact that most of the enemies in this game are clumped in large groups that just charge at you all at once is really not helping things here either. It is thanks to all these gameplay flaws that the foundation of the gameplay of this Fire Emblem is completely shattered.
I am able to understand why a lot of people like this game though, since it has a story that provides a fair amount of impactful moments, alongside with having a phenomenal soundtrack. Considering that I hold gameplay in high regard for the Fire Emblem series though, I can't see this game being anything but terrible. After the experience of a first playthrough that allows one to enjoy the story and the soundtrack, all that is left is a massively flawed game.