The main difference is in their range. Both specialize in charged attacks; whilst Yanfei drops an anvil on top of the enemy from a pretty decent range, Klee fires a projectile at a downward angle and can't seem to hit very far (from what I've heard). Even with normal attacks, Yanfei throws a targeted fireball with significant range, whereas Klee throws an arcing projectile, and thus has more limited range (and also it deals like 3 damage apparently).
EDIT Thanks to SPArcheon for reminding me of this as well. Klee also has a ton of animation cancels with just about anything she does - her slow animations actually caused her to be considered bad for some time until people learned the cancels. On the other hand, Yanfei doesn't really have that. Her animations are a bit faster, but you can't cancel as nicely. Her normal attack comes out quickly enough that there's no point cancelling. If you jump or sprint after summoning her anvil (charged attack), it will just disappear (there's actually even a special animation for the anvil dissipating from being canceled). You can still cancel it if you wait until just as the anvil starts falling, but her charged attacks are fast enough even back-to-back that there's no point.
Yanfei also has ~~Star Jades~~ Scarlet Seals, which is a mechanism Klee doesn't have. Doesn't really change the similarity in their playstyle but just something else to note.
Klee's charged attacks are bombs whereas Yanfei's is just Pyro damage - the distinction is that Klee can break Geo constructs and shields (thanks to Steven for this point). I forget about Klee's normal attacks and whether or not they deal AOE / are bombs, but Yanfei's normal attacks are targeted and only deal Pyro.
Klee's E is a deployable, whereas Yanfei's E is a burst ability.
Their bursts slightly differ in that Yanfei buffs herself but Klee just deploys damage automatically; this is not too significant of a difference since both just increase damage and force you to keep them active lest you dispel your ultimate early.
Their ascension passives aren't different by a significant amount - Yanfei gains PYRO% and deals bonus damage; Klee deals bonus damage and reduces stamina cost, and gains Energy for her party.
Finally, their constellations pretty much just do damage, more damage, and even more damage.
So, overall, I agree with you that there's very limited differences. Their ascensions and constellations are basically just "damage and a ton more damage", and their abilities differ pretty much only on technicalities.
TL;DR: The main obvious difference that I noticed right away, even only having played Klee during story quests and character trials, is that Yanfei has significantly longer range, Klee requires more timing with animations whereas Yanfei just has smoother animations, and Klee can break Geo constructs and stagger a lot more heavily than Yanfei can.
Best Answer
EDIT:Thanks to Childe,just find out a huge mistake of mine. I have calculate the 247 EM wrong. It should only provide 41.7%, not 58.7%. Also, I have Added the calculation of damage for using Mappa Mare.
You should use elemental mastery if you have Xingqiu and using a weapon that provide percentage ATK(Or if you use Bennett.).
Let's do some math.
Yanfei base attack at level 90 is 240, let's use Three weapon, Favonius Codex,Memory of Dust,and Lost Prayer to the Sacred Winds to calculate damage for Yanfei's charge attack at talent level 10(without calculating scarlet, damage increase, and crits) for ATK sand and EM sand. Let's made up a sub-stats for Artifacts, 30% ATK increase, 60 EM, 50 ATK total.
Favonius Codex: 4 star weapon,provide 510 base attack on 90 level, no percentage attack increase.
ATK sand:grant 46.6% ATK increase, adding 30% from sub-stats, which will provide 76.6%750=574~575 ATK. Total attack equals 750+575+311(From Feather)+50(From sub-stats)=1686 attack. 60 EM from sub-stats equals 11.4% damage increase for Vaporize, and using 4 WoF artifact will increase Vaporize by 15%, total increase is 26.4%. Damage without calculating damage increase, critical, and defense is 16861.5(vaporize)*1.264(vaporize damage increase)*1.8822(skill)=6016~6017 damage.
EM sand: grant 187 EM,which is 247 EM total,brings us 41.7% vaporize damage increase,adding 4 WoF artifact to it equals 56.7% increase. And the ATK from percentage attack is 750*0.3=225. The finial ATK is 750+225+50+311=1336. Final damage is 1336 * 1.5 * 1.567 * 1.8822=5910~5911
Memory of Dust:5 star weapon,provides 608 base ATK,49.6 percentage attack.
ATK sand:grant 46.6 percentage attack,total up to 126.6 percentagr attack,which is 848*1.266=1073~1074 ATK. Final attack is 848+1074+50+311=2283 ATK. Base on other information from previous part,final damage is 2283 * 1.5 * 1.264 * 1.8822=8147 damage.
EM sand :56.7% Vaporize damage increase,79.6% attack increase. 848*0.796=675 ATK,final ATK is 848+675+50+311=1884 ATK. Final damage 1884 * 1.5 * 1.567 * 1.8822=8335.
Lost Prayer to the Sacred Winds:5 star weapon, provide 608 base ATK.
ATK sand: total percent attack increase is 76.6%, which means 649~650 ATK. Final ATK is 848+650+50+311=1859. Final damage equals 1859 * 1.5 * 1.266 * 1.8822=6644~6645.
EM sand: total percent attack increase is 30%. Final attack is 848+254+50+311=1463. Final damage is 1463 * 1.5 * 1.567 * 1.8822=6472.
So from those three calculation,if your weapon have percentage ATK,you should use EM sand because the ATK is been delute. And if you have a lot ATK increase from sub-stat of artifact and no EM,you could use it too.
Then,if you use Bennett,use EM sand too. Let‘s do the calculation again on Lost Prayer to the Sacred Winds. A 10 level elemental burst bennett with Prototype Rancour will provide 764 Attack(Base Attack 756*101%)
By the way, keep in mind that the damage is only for comparing EM sand and ATK sand, not for weapon compare, so don’t say that Memory of Sand is better than Lost Prayer to the Sacred Winds base on my calculations. My calculation didn’t count the damage increase(fire damage increase and other) and critical damage, those will not effect ATK and EM comparison, but will surely effect weapon comparison.
ADDED:
Mappa Mare: 4 star weapon, provide 565 base attack and 100 EM.